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Faculty details

Prof.Akhilesh Prasad

Designation: Professor

Department: Mathematics & Computing

Email: aprasad[at]iitism[dot]ac[dot]in

Contact Number:

Office Number: +91-326-223-5666

Personal Page: Click Here

About Me: I am a Professor in the Department of Mathematics and Computing since June 2019. Previously, I have worked as Associate Professor (September, 2010-June, 2019) and Assistant Professor (September, 2007-Sptember, 2010) at the same Institute. I have also worked as Post-Doctoral Fellow under DST-Fast Track Proposal for Young Scheme (December, 2004 -September, 2007) at Banaras Hindu University Varanasi, India and Lecturer (August, 2003 to November, 2004) at Jagatpur P.G. College Varanasi affiliated to Purvanchal University Jaunpur, India. I did my Ph.D in Mathematics from the Department of Mathematics, Banaras Hindu University Varanasi, India in 2002.

Research Interest: Integral Transforms, Pseudo-Differential Operators, and Wavelet Analysis.

Curriculum
Vitae
Publications

Teaching

Integral Transforms

Functional Analysis

Real Analysis

Complex Analysis

Wavelet Transform

Functional Analysis

Integral Equation and Calculus of Variations.

Academics

Educational Qualifications:  Uniform Academic Records with First Division from High  School to M.Sc.

Ph.D. :                                    Awarded in 2002 from Department of Mathematics, Banaras Hindu University, Varanasi-221005  

Title of Ph. D Thesis:           Pseudo-Differential Operators on Gevrey Spaces                                

Research Interest:               Integral Transforms, Pseudo- Differential Operators, Wavelets, Distribution Theory

Position

  1. Professor, Department of Mathematics & Computing, IIT (ISM)-Dhanbad continuously since June 06, 2019.
  2. Associate Professor, Department of Applied Mathematics, IIT (ISM)-Dhanbad since September 07, 2010 to June 05, 2019.
  3. Assistant Professor, Department of Applied Mathematics, ISM-Dhanbad since September 07, 2007 to September 06, 2010.
  4. Post-Doctoral Fellow/Principal Investigator under DST SERC FAST TRACK Proposal for Young Scientists Scheme at Department of Mathematics, Banaras Hindu University, Varanasi since December 2004 to September 06, 2007.
  5. Lecturer, Department of Mathematics, Jagatpur P.G College Varanasi, affiliated to V.B.S. Purwanchal University, Jaunpur since August 2003 to November 2004.
  6. Research Scholar, Department of Mathematics, BHU-Varanasi since January 1998 to February 2002.

Awards and Honors

Editorship:

1. Asian-European Journal of Mathematics (World Scientific Publishing)/ (Since November 2024)

Travel Grants for International Conference/Collaboration work:


1. International Society for Analysis, its Applications and Computation (ISAAC 2023), University of Sao Paulo, Campus Ribeirao Preto, Brazil. [SERB: MATRICS
   Project No.: MTR/2021/000193] (2023).
2. International conference on Subdivision; Geometric and Algebraic Methods; Isogeometric Analysis and Refinability, (SMART 2022), University of Bologna, Italy at
    Rimini, Italy. [IIT (ISM)] (2022).
3. Collaboration work at Steklov Mathematical Institute / People Friendship University, Moscow, Russia under Indo-Russian project under grant no. INT/RU/RSF/P-
    01 (2018)
4. International conference ”Strobl18” Harmonic Analysis and Applications, Strobl, Austria [IIT (ISM)] (2018)
5. 7th Conference on Function Spaces at Southern Illinois University, Edwardsville, USA [ISM + Host Institute] (2014).
6. International Conference on Applied & Computational Mathematics at Ankara, Turkey [CSIR + ISM] (2012).
7. International Conference on Applied Mathematics & Approximation Theory at Ankara, Turkey, ISM (2012).
8. International Congress of Mathematician (ICM-2010) at Hyderabad - ICM-(2010).
9. International Conference on Approximation Theory and Signal Analysis at Lindau, Germany, ISM (2009).
10. International Conference at Halmholtz Zenturm Munchen, Germany, [DST + Host Institute] (2007).

Reviewer of Some Reputed Journals:

  1. Applicable Analysis (Taylor & Francis)
  2. Applied Mathematics (Scientific Research)
  3. Analysis Mathematica (Springer)
  4. Asian-European Journal of Mathematics (World Scientific)
  5. Banach Journal of Mathematical Analysis (Springer-Birkhauser)
  6. Bulletin of the London Mathematical Society
  7. Complex Analysis and Operator Theory (Springer-Birkhauser)
  8. Complex Variables and Elliptic Equations (Taylor & Francis)
  9. Filomat
  10. Fixed Point Theory and Applications (Springer)
  11. International Journal of Wavelets, Multiresolution and Information Processing (World Scientific)
  12. Integral Transforms and Special Functions (Taylor & Francis)
  13. Journal of Analysis (Springer)
  14. Journal of Function Spaces (Hindawi)
  15. Journal of Indian Mathematical Society
  16. Journal of Inequalities and Applications (Springer)
  17. Journal of Mathematics (Hindawi)
  18. Journal of Pseudo-Differential Operators and Applications (Springer-Birkhauser)
  19. Mathematical Methods in the Applied Sciences (Wiley)
  20. Mathematical Reviews (American Mathematical Society)
  21. National Academy Science Letters (Springer)
  22.  Proceedings of the National Academy of Sciences, India Section A: Physical Sciences (Springer)
  23. Pure and Applied Mathematics Quarterly (International Press)
  24. Ramanujan Journal (Springer)
  25. Results in Mathematics (Springer-Birkhauser)
  26. Revista de la Real Academia de Ciencias Exactas, F´ısicas y Naturales. Serie A. Matema´ticas (Springer)
  27. Rocky Mountain Journal of Mathematics (Cornell University)
  28. Science China Mathematics (Springer)
  29. Transactions on Signal Processing (IEEE)
  30. Zentralbatt Maths (European Mathematical Society)
  31. Applied Mathematics Letter (Elsevier)
  32. Boletim da Sociedade Paranaense de Matema´tic
  33. Investigations of Mathematical Sciences
  34. Thai Journal of Mathematics

Publications

Books Published

1. Pseudo-Differential Opererators on Gevrey Spaces, VDM Verlag, Germany, 2009.

 

List Of Research Publications (only in Peer-reviewed Journals)

  1. Akhilesh Prasad, S. Ranjan, An operational calculus of µth order Mehler-Fock transform, Complex Anal. Oper. Theory, 19 (2), pp. 1-33, (2025). (Springer- Birkhauser).
  2. R. K. Verma and Akhilesh Prasad, Besov-type spaces associated with Dunkl wavelet transform on R, Math. Methods Appl. Sci., DOI: 10.1002/mma.10769, (2025). (Wiley).
  3. Akhilesh Prasad, U. K. Mandal and S. Ranjan, The µth order Mehler-Fock trans- form and allied pseudo-differential operator, Integral Transforms Spec. Funct., 36 (3), pp. 163-175, (2025). (Taylor & Francis).
  4. C. Roy, T. Kumar, Akhilesh Prasad, and G. K. Jha, Pseudo-differential opera- tors associated with a pair of quadratic-phase Hankel transformations, J. Pseudo- Differ. Oper. Appl., 16 (1), Article number: 05, pp. 1-26, (2025). (Springer- Birkhauser)/ SCIE.
  5. A. K. Gupt and Akhilesh Prasad, The Heat Kernel in the Framework of the Lebedev-Skalskaya Transform, Appl. Anal., DOI: 10.1080/00036811.2024.2431613, (2024). (Taylor & Francis)/SCIE.
  6. K. L. Mahato, S. Arya and Akhilesh Prasad, Pseudo-differential operators as- sociated with Gyrator transform, Hacet. J. Math. Stat., DOI: 10.15672/hu- jms.1471348, (2024). (DergiPark).
  7. S. Varghese, Akhilesh Prasad and M. Kundu, Properties and applications of quaternion quadratic phase Fourier transforms, J. Pseudo-Differ. Oper. Appl., 15 (4), Article number: 84, pp. 1-26 (2024). (Springer-Birkhauser).
  8. R. K. Verma and Akhilesh Prasad, SG pseudo-differential operators in Dunkl setting, Georgian Math. J., DOI: 10.1515/gmj-2024-2072, (2024). (De Gruyter).
  9. C. Roy, T. Kumar,Akhilesh Prasad, and G. K. Jha, The wavelet transformation associated with quadratic-phase Hankel transform, Natl. Acad. Sci. Lett. DOI: 10.1007/s40009-024-01423-2, (2024). (Springer).
  10. Akhilesh Prasad and M. Kundu, Spectrum of quaternion signals associated with quaternion linear canonical transform, J. Franklin Inst., 361 (2), pp. 764-775 (2024). (Elsevier).
  11. A. K. Gupt, U. K. Mandal and Akhilesh Prasad , Lebedeb-Skalskaya transform related continuous wavelet transform, Results Math., 79 (3), Article number: 99, pp. 1-21 (2024).  (Springer-Birkhauser).
  12. A. K. Gupt and Akhilesh Prasad, The infinite-order integro-differential operator related to Lebedev-Skalskaya transform, J. Pseudo-Differ. Oper. Appl., 15 (2), Article number: 21, pp. 1-16 (2024). (Springer-Birkhauser)
  13. Akhilesh Prasad, R. K. Verma and S. K. Verma, Wavelet transform associated with Dunkl transform, Integral Transforms Spec. Funct. 35 (9), pp. 481-496, (2024). (Taylor & Francis).
  14. J. S. Maan and Akhilesh Prasad, A pair of pseudo-differential operators involving index Whittaker transform in La(R+; ma(x)dx), Acta Math. Sin. (Engl. Ser.), 40 (6), pp. 1420–1430, (2024). (Springer).
  15. J. S. Maan and Akhilesh Prasad, Wave packet transform and wavelet convolution product involving index Whittaker transform, Ramanujan J., 64 (1), pp. 19-36, (2024). (Springer).
  16. J. S. Maan and Akhilesh Prasad, Index Whittaker transform for Boehmians, Indian J. Pure Appl. Math., 55(2), pp. 489-500-315 (2024). (INSA/Springer).
  17. Akhilesh Prasad and R. K. Verma, Weyl transforms associated with Dunkl wavelet transform, Complex Anal. Oper. Theory, 17 (7), Article number: 110, pp. 1-17, (2023).  (Springer-Birkhauser).
  18. U. K. Mandal and Akhilesh Prasad, The generalized Kontorovich-Lebedev trans- form and associated operators, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. RACSAM, 117 (3), Article: 126, pp. 1-15, (2023). (Springer).
  19. M. Kundu and Akhilesh Prasad, Pseudo-differential operator in quaternion space, Math. Methods Appl. Sci., 46(9), pp. 10749-10766, (2023). (Wiley).
  20. Akhilesh Prasad and M. Kundu , Uncertainty principles and applications of quaternion windowed linear canonical transform, Optik, 272(1), Article number: 170220 (2023). (Elsevier).
  21. Akhilesh Prasad and A. Kumar, Canonical potential and Lp-Sobolev space in- volving linear canonical Fourier transform, Integral Transforms Spec. Funct. 34(4), pp. 295-315 (2023). (Taylor & Francis).
  22. A. K. Gupt, Akhilesh Prasad and U. K. Mandal, The fractional maximal and Riesz potential operators involving the Lebedev-Skalskaya transform, Proc. Natl. Acad. Sci., Sect. A Phys. Sci., 93 (4), pp. 613-620, (2023). (Springer) / SCIE.
  23. A. Kumar, Akhilesh Prasad and P. Jain, The Weyl correspondence in the linear canonical transform domain, Filomat,, 37 (22), pp. 7431-7444, (2023). (SCIE)
  24. P. B. Sharma and Akhilesh Prasad, Abelian theorems for quadratic-phase Fourier wavelet transform, Proc. Natl. Acad. Sci., Sect. A Phys. Sci., 93 (1), pp. 75-83, (2023). (Springer).
  25. U. K. Mandal, Akhilesh Prasad and A. K. Gupt, Reverse convolution inequalities for Lebedev-Skalskaya transforms, Forum Math., 34 (4), pp. 1095-1107 (2022). (De Gruyter).
  26. A. Kumar and Akhilesh Prasad, Wigner-Ville distribution function in the frame- work of linear canonical transform, J. Pseudo-Differ. Oper. Appl., 13 (3), Article number: 38, pp. 1-17 (2022). (Springer-Birkhauser).
  27. M. Kundu and Akhilesh Prasad, Uncertainty principles associated with quater- nion linear canonical transform and its estimates, Math. Methods Appl. Sci., 45 (8), pp. 4772-4790, (2022). (Wiley).
  28. M. Kundu and Akhilesh Prasad, Convolution, correlation and spectrums of func- tions associated with linear canonical transform, Optik, 249 (1) Article ID: 168256 (2022). (Elsevier).
  29. J. S. Maan and Akhilesh Prasad, Abelian theorems in the framework of distri- butional index Whittaker transform, Math. Commun. 27 (1), pp. 1-9, (2022).
  30. U. K. Mandal and Akhilesh Prasad, Lebedev-Skalskaya transforms and allied operators on certain function spaces, Integral Transforms Spec. Funct. 33 (4), pp. 320-340, (2022). (Taylor & Francis).
  31. Akhilesh Prasad and Manoj K. Singh, Product and commutators of pseudo- differential operators involving Fourier-Jacobi transform, Comm. Math. Stat. 10 (1), pp. 67-84 (2022). (Springer).
  32. Akhilesh Prasad and Z. A. Ansari, The wave packet transform in the framework of linear canonical transform, Int. J. Wavelets Multiresolut. Inf. Process., 20 (2), Article No. 1500521, (16 pp.) (2022). (World Scientific).
  33. J. S. Maan and Akhilesh Prasad, Weyl operator associated with index Whittaker transform, J. Pseudo-Differ. Oper. Appl., 13 (3), Article number: 27, (2022). (Springer-Birkhauser).
  34. P. B. Sharma and Akhilesh Prasad, Convolution and product theorems for the quadratic-phase Fourier transform, Georgian Math. J., 29 (4), pp. 595-602, (2022). (De Gruyter).
  35. M. Kundu, Akhilesh Prasad, and R. K. Verma, Multidimensional linear canonical transform and convolution, J. Ramanujan Math. Soc. 37 (2), pp. 159-171, (2022).
  36. Akhilesh Prasad, J. S. Maan and S. K. Verma, Wavelet transforms associated with the index Whittaker transform, Math. Methods Appl. Sci., 44 (13), pp. 10734-10752, (2021). (Wiley).
  37. Z. A. Ansari and Akhilesh Prasad, Abelian theorems and Caldero´n’s reproducing formula for linear canonical wavelet transform, J. Pseudo-Differ. Oper. Appl., 12 (1), Article: 4, (2021). (Springer-Birkhauser).
  38. U. K. Mandal and Akhilesh Prasad, Lebedev-Skalskaya transforms on certain function spaces and associated pseudo-differential operators, Integral Transforms Spec. Funct., 32 (2), pp. 113-133, (2021), (Taylor & Francis).
  39. Akhilesh Prasad, and U. K. Mandal, The Kontorovich-Lebedev-Clifford trans- form, Filomat. 34 (14), pp. 4811-4824 (2021).
  40. T. Kumar and Akhilesh Prasad, Pseudo-differential operators involving linear canonical Hankel transformations on some ultra-differentiable function spaces, Math. Methods Appl. Sci., 44 (6), pp. 4686-4700, (2021). (Wiley).
  41. Akhilesh Prasad and M. Kundu, Linear canonical wave packet transform, Integral Transforms Spec. Funct., 32 (11), pp. 893-911, (2021), (Taylor & Francis).
  42. Akhilesh Prasad, T. Kumar and A. Kumar, Convolution for a pair of quadratic- phase Hankel transforms, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. RACSAM, 114 (3), Article: 40, pp. 1-15, (2020). (Springer).
  43. S. K. Verma and Akhilesh Prasad, Characterization of Weyl operator in terms of Mehler-Fock transform, Math. Methods Appl. Sci., 43 (15), pp. 9119-9128, (2020). (Wiley).
  44. Akhilesh Prasad and Z. A. Ansari, The composition of linear canonical wavelet transforms on generalized function spaces, Filomat, 34 (12), pp. 2457-2469, (2020).
  45. Akhilesh Prasad and P. B. Sharma, The Quadratic-Phase Fourier Wavelet Trans- form, Math. Methods Appl. Sci., 43 (4), pp. 1953-1969, (2020). (Wiley).
  46. Akhilesh Prasad and P. K. Maurya, The fractional Hankel-type integral wavelet packet transformation, J. Anal., 28 (1), 225-234 (2020) (Springer).
  47. Akhilesh Prasad and Z. A. Ansari, Approximation of linear canonical wavelet transform on the generalized Sobolev spaces, J. Pseudo-Differ. Oper. Appl. 10 (4), pp. 855-881, (2019). (Springer-Birkh¨auser).
  48. Akhilesh Prasad, P. Kumar and T. Kumar, Product of continuous fractional wave packet transforms, Int. J. Wavelets Multiresolut. Inf. Process., 17 (4), Article ID: 1950021 (09 pages), (2019). (World Scientific).
  49. Akhilesh Prasad, U. K. Mandal and S. K. Verma, Zero-order Mehler-Fock trans- form and Sobolev- type space, Math. Inequal. Appl., 22 (2), pp. 761-775. (2019).
  50. Akhilesh Prasad and S. K. Verma, Heat kernel in the framework of zero order Mehler-Fock transform, Complex Anal. Oper. Theory, 13 (7), pp. 3235-3249. (2019), (Springer-Birkh¨auser).
  51. Akhilesh Prasad and T. Kumar, A pair of linear canonical Hankel transforma- tions of random order, Mediterr. J. Math., 16 (6) Article 150 (18 pages), (2019), (Springer-Birkh¨auser).
  52. Akhilesh Prasad and Z. A. Ansari, Continuous wavelet transform involving lin- ear canonical transform, Natl. Acad. Sci. Lett. 42 (4), pp. 337-344. (2019), (Springer).
  53. Akhilesh Prasad and S. K. Verma, The Mehler-Fock-Clifford transform and pseudo-differential operator on function spaces, Filomat, 33 (8), pp. 2457-2469, (2019).
  54. Akhilesh Prasad and Manoj K Singh, Composition of pseudo-differential opera- tors associated with Jacobi differential operator, Proc. Natl. Acad. Sci., Sect. A Phys. Sci., 89 (3), pp. 509-516, (2019). (Springer).
  55. Akhilesh Prasad and U. K. Mandal, Two versions of pseudo-differential operators involving Kontorovich-Lebedev transform in L2(R+; x−1dx), Forum Math., 30 (1), pp. 31-42, (2018). (De Gruyter).
  56. Akhilesh Prasad and T. Kumar, A pair of linear canonical Hankel transfor- mations and associated pseudo-differential operators, Appl. Anal., 97 (15), pp. 2727-2742, (2018). (Taylor & Francis).
  57. Akhilesh Prasad and U. K. Mandal, The Kontorovich-Lebedev transform and its associated pseudo-differential operator, Math. Methods Appl. Sci., 41 (1), pp. 46-57, (2018). (Wiley).
  58. Akhilesh Prasad, S. K. Verma and U. K. Mandal, The convolution for zero order Mehler-Fock transform and pseudo-differential operator, Integral Transforms Spec. Funct., 29 (3), pp. 189-206 (2018). (Taylor & Francis).
  59. Akhilesh Prasad and S. K. Verma, Continuous wavelet transform associated with zero order Mehler-Fock transform and its composition, Int. J. Wavelets Multireso- lut. Inf. Process., 16 (6), Article ID: 1850050 (16 pages), (2018). (World Scien- tific).
  60. Akhilesh Prasad and U. K. Mandal, The Kontorovich-Lebedev transform and Sobolev type spaces, Complex Anal. Oper. Theory, 12 (3), pp. 669-681, (2018). (Springer-Birkh¨auser).
  61. Akhilesh Prasad and K. Mahato, On the Sobolev boundedness results of the prod- uct of pseudo-differential operators involving a couple of fractional Hankel trans- forms, Acta Math. Sin. (Engl. Ser.), 34 (2), pp. 221-232, (2018). (Springer).
  62. Akhilesh Prasad and T. Kumar, Canonical Hankel wavelet transformation and Caldero´n’s reproducing formula, Filomat, 32 (8), 2735-2743, (2018). .
  63. Akhilesh Prasad and U. K. Mandal, Boundedness of pseudo-differential operators involving Kontorovich-Lebedev transform, Integral Transforms Spec. Funct., 28 (4), pp. 300-314, (2017). (Taylor & Francis).
  64. Akhilesh Prasad and U. K. Mandal, Wavelet transforms associated with the Kontorovich-Lebedev transform. Int. J. Wavelets Multiresolut. Inf. Process., 15 (2), Article ID: 1750011 (17 pages) (2017). (World Scientific).
  65. Akhilesh Prasad and Manoj. K. Singh, Pseudo-differential operators involving fractional Fourier cosine (sine) transform, Filomat, 31 (6), pp. 1791-1801, (2017).
  66. D. C. Mishra, R. K. Sharma, S. Suman and Akhilesh Prasad, Multi-layer security of color image based on chaotic system combined with RP2DFRFT and Arnold Transform, J. Info. Sec. Appl. 37(6), pp. 65-90, (2017), (Elsevier).
  67. Akhilesh Prasad and P. K. Maurya, A couple of fractional powers of Hankel- type integral transformations and pseudo-differential operators, SeMA. 74 (2), pp. 181-211, (2017)(Springer).
  68. Akhilesh Prasad and U. K. Mandal, Composition of pseudo-differential operators associated with Kontorovich-Lebedev transform, Integral Transforms Spec. Funct., 27 (11), pp. 878-892, (2016). (Taylor & Francis).
  69. Akhilesh Prasad and P. Kumar, Composition of pseudo-differential operators associated with fractional Hankel-Clifford integral transformations, Appl. Anal. 95 (8), pp. 1792-1807, (2016). (Taylor & Francis).
  70. Akhilesh Prasad and P. Kumar, The continuous fractional wavelet transform on a generalized Sobolev space, Int. J. Wavelets Multiresolut. Inf. Process., 14 (6), Article ID: 1650046 (10 pages), (2016) (World Scientific).
  71. Akhilesh Prasad and S. Kumar, Fractional wavelet packet transformations in- volving Hankel-Clifford integral transformations, Acta Math. Sin. (Engl. Ser.) 32 (7), pp. 783-796, (2016). (Springer).
  72. Akhilesh Prasad and P. Kumar, Pseudo-differential operator associated with fractional Fourier Transform, Math. Commun. 21 (1), pp. 115-126, (2016).
  73. Akhilesh Prasad and P. Kumar, Composition of continuous fractional wavelet transforms, Natl. Acad. Sci. Lett. 39 (2), pp. 115-120, (2016). (Springer).
  74. Akhilesh Prasad and S. Kumar, A pair of fractional powers of Hankel-Clifford transformations of arbitrary order, Filomat, 30 (12), pp. 3303-3316, (2016).
  75. Akhilesh Prasad and P. Kumar, Fractional continuous wavelet transform on some function spaces., Proc. Natl. Acad. Sci., Sect. A Phys. Sci., 86 (1), pp. 57-64, (2016). (Springer).
  76. Akhilesh Prasad and P. K. Maurya, A pair of pseudo-differential operators in- volving Hankel-type integral transformations, J. Pseudo-Differ. Oper. Appl., 6(1), pp. 135-151, (2015). (Springer-Birkh¨auser).
  77. Akhilesh Prasad and S. Kumar, Wavelet transformation associated with second Hankel-Clifford transformation, Natl. Acad. Sci. Lett., 38 (6), pp. 493-496, (2015). (Springer).
  78. Akhilesh Prasad, S. Manna, A. Mahato and V. K. Singh, The generalized con- tinuous wavelet transform associated with fractional Fourier transform, J. Comput. Appl. Math. 259, pp. 660-671, (2014). (Elsevier).
  79. Akhilesh Prasad and V. K. Singh, Boundedness of pseudo-differential operator associated with fractional Hankel transform, Fract. Cal. Appl. Anal. 17 (1), pp. 154-170, (2014). (Springer/De Gruyter).
  80. Akhilesh Prasad and S. Kumar, Two variants of fractional powers of Hankel- Clifford transformations and pseudo-differential operators, J. Pseudo-Differ. Oper. Appl. 5 (3), pp. 411-454, (2014). (Springer-Birkh¨auser).
  81. Akhilesh Prasad and M. Kumar, Boundedness of pseudo-differential operator associated with fractional Fourier transform, Proc. Natl. Acad. Sci., Sect. A Phys. Sci., 84 (4), pp. 449-454, (2014). (Springer).
  82. Akhilesh Prasad and A. Mahato, The fractional wavelet transform on spaces of type W, Integral Transforms Spec. Funct., 24 (3), pp. 239-250, (2013). (Taylor & Francis).
  83. Akhilesh Prasad and S. Kumar, Hankel-Clifford transformations on some ultra- differentiable function spaces and pseudo-differential operators, J. Pseudo-Differ. Oper. Appl. 4 (4), pp. 551-567, (2013). (Springer-Birkh¨auser).
  84. Akhilesh Prasad, A. Mahato, V. K. Singh and M. M. Dixit, The continuous fractional Bessel wavelet transformation, Bound. Value Probl., 2013: 40 (16 pages), (2013). (Springer).
  85. Akhilesh Prasad, A. Mahato and M. M. Dixit, Continuity of Bessel wavelet transform on certain Beurling-type function spaces, J. Inequal. Appl., 2013: 29, (9 pages), (2013). (Springer).
  86. Akhilesh Prasad, A. Mahato, The fractional wavelet transform on spaces of type S., Integral Transforms Spec. Funct., 23 (4), pp. 237-249, (2012). (Taylor & Francis).
  87. R. S. Pathak, Akhilesh Prasad and M. Kumar, Fractional Fourier transform of tempered distributions and generalized pseudo-differential operator, J. Pseudo- Differ. Oper. Appl. 3 (2), pp 239-254, (2012). (Springer-Birkh¨auser).
  88. Akhilesh Prasad, M. Kumar and D. R. Chaudhary, Color image encoding us- ing fractional Fourier transformation associated with wavelet transformation, Opt. Commun. 285(6), pp. 1005-1009, (2012), (Elsevier).
  89. R. S. Pathak, Akhilesh Prasad and M. Kumar, An n-Dimensional pseudo–differential operator hµ,a involving the Hankel transformation, Proc. Indian Acad. Sci. (Math. Sci.), 122 (1), pp. 99–120, (2012), (Springer).
  90. R. S. Pathak, Akhilesh Prasad and M. Kumar, n- Dimensional Sobolev type spaces involving Hankel transformation, Appl. Math. Comput., 218(3), pp. 899- 905, (2011) (Elsevier).
  91. Akhilesh Prasad and M. Kumar, Product of two generalized pseudo-differential operators involving fractional Fourier transform, J. Pseudo-Differ. Oper. Appl., 2(3), pp. 355-365, (2011). (Springer-Birkh¨auser).
  92. Akhilesh Prasad and M. Kumar, Continuity of pseudo-differential operator hµ,a involving Hankel translation and Hankel convolution on some Gevrey spaces, Inte- gral Transforms Spec. Funct., 21(6), pp. 465-477, (2010). (Taylor & Francis).
  93. R. S. Pathak and Akhilesh Prasad, A generlized pseudo-differential operator on Gel’fand-Shilov space and Sobolev space, Indian J. Pure Appl. Math., 37(4), 223-235, (2006). (INSA/Springer).
  94. R. S. Pathak and Akhilesh Prasad, The pseudo-differential operator hµ,a on some Gevrey spaces, Indian J. Pure Appl. Math. 34(8), pp. 1225-1236, (2003). (INSA/Springer).
  95. R. S. Pathak and Akhilesh Prasad, The pseudo-differential operator hµ,a on Hankel invariant spaces, Appl. Anal. 82(2), pp. 187-196, (2003). (Taylor & Francis).
  96. R. S. Pathak and Akhilesh Prasad, Continuity of pseudo-differential operators associated with the Bessel operators in some Gevrey spaces, Appl. Anal. 81(3), pp. 637- 662, (2002). (Taylor & Francis).

Papers in conference abstract volumes / presented

1. Akhilesh Prasad, Manoj K. Singh and M. Kumar, The continuous fractional wave packet transform, AIP Conf. Proc. 1558, pp. 856-859 (2013). (AIP)/Scopus.

Projects & Activities

Sponsored Research Projects (External Funded)

Sponsored Projects as PI (Running / Handled):

S. N.

Name of the Agency

Title of Project

Started -Completed

Total Cost (Rs)

Institution

1

          SERB

       Project No.: MTR/2021/000193

Linear Canonical Transform and associated Wavelets and Wavelet Transform

February 23, 2022 -February 22, 2025

6,60,000/-

Department of Mathematics & Computing, IIT (ISM), Dhanbad-826004

2

    NBHM (DAE)

      Project No.:   020011/7/2021 NBHM (R.P)/ R&D II/8164

The pth order Mehler-Fock transform and some related operators on function spaces

April 01, 2021 - March 31, 2024

16,49,533/-

Department of Mathematics & Computing, IIT (ISM),

Dhanbad-826004

3

    DST-SERB

File No.: EMR/ 2016/005141/MS

The Kontorovich-Lebedev Transform and related Integral Operators on Function and Distribution Spaces

March 16, 2018- March 15, 2021

15,79,094/-

Department of Mathematics & Computing, IIT (ISM),

Dhanbad-826004

4

           CSIR:

       Project No.: 25(240)/15/

       EMR-II

A Pair of Fractional Powers of Bessel Wavelet Transform and associated Wavelets

October 01, 2015- September 30, 2018

17,17,800/-

Department of Applied Mathematics, IIT (ISM),

Dhanbad-826004

5

NBHM (DAE): Project No.: 2/48 (14)/2011/ R&D -II/3501

Pseudo-Differential Operators and Wavelet Transform Involving Fractional Fourier Transform on Function and Distribution Spaces

April 01, 2012- March 31, 2015

10,07,500/-

Department of Applied Mathematics, ISM,

Dhanbad-826004

6

         UGC:

Project No.: 34-145/2008(SR)

Pseudo-differential operators associated with Bessel Operator on Gevrey Spaces

February 01, 2009- January 31, 2012

6,02,345/-

Department of Applied Mathematics, ISM,

Dhanbad-826004

7

IIT (ISM) Project No.: MRP(AM)/ Acad/05/2008

A pseudo-differential operator involving Hankel transform on Gevrey Spaces

August 01, 2008- July 31, 2010

1,00,000/-

Department of Applied Mathematics, ISM,

Dhanbad-826004

8

DST: Project No.: SR/FTP/ MS-07/2003

Pseudo-differential operators and the Hankel transform on Gevrey Spaces

December 01, 2004- September 06, 2007

9,25,000/-

Department of Mathematics, BHU, Varanasi-221005

Sponsored International Project as Co-PI (Running /Handled):

S. N.

Name of the Agency

Title of Project

Started -Completed

Total Cost (Rs)

Institution

1

DST: Project No. INT/RU/RSF/P-01 (Indo-Russian S&T Project)

Classical operators on Sobolev and Banach function spaces and Quasi-conformal analysis

October 05, 2016- October 04, 2019

41,51,400/-

Department of Mathematics, South Asian University, New Delhi-110021

Consultancy Project (for ONGC)

Training Programme/Workshop/Conferences/Lectures/other academic meets Organized:

1. Organized a ”National Conference on Harmonic Analysis and Applications”, during December 02-04, 2022 as a convener.
2. Organized a Short Term Advanced Training Programme on ”Integral Transformations, Distributions, Wavelet Analysis and Applications” (Phase-II), during October
    08-12, 2018 as a coordinator.
3. Organized a Short Term Training Programme on ”Non-linear Analysis and Optimization”, during December 01-05, 2017 as a co-coordinator.
4. Organized a Short Term Training Programme on ”Nonlinear Analysis and its Application to Optimization Techniques”, during August 18 - 22, 2017 as a cocoordinator.
5. Organized a Short Term Advanced Training Programme on ”Integral Transformations, Distributions and Wavelet Analysis”, during December 14-18, 2015 as a coordinator.
6. A talk of Prof. (Retd.) P. K. Jain (F.N.A.Sc), University of Delhi on topic “Schauder Decompositions and Frames in Banach Spaces” was organised on February 9, 2012 at 3:30        PM in the Management Study Hall.
 

Membership of Scientific Societies

  1. Fellow-Institute of Mathematics and its Applications (FIMA)
  2. Life Membership of International Society for Analysis, Its Applications and Computations (ISAAC)
  3. Annual Membership of American Mathematical Society.
  4. Life Membership of the Indian Science Congress Association.
  5. Life membership of Indian Mathematical Society.
  6. Life Membership of Ramanujan Mathematical Society.
  7. Life membership of Calcutta Mathematical Society
  8. Life membership of Mathematical Society Banaras Hindu University, Varanasi.
  9. Life membership of Academy of Progress of Mathematics, Banaras Hindu University, Varanasi.
  10. Life membership of Society of Applied Mathematics, Indian School of Mines, Dhan- bad.

Other Academic and Administrative Activities

Other Information (Organizational/Committee/ Administrative Work):

(I-Internal):

1.   Departmental Time-Table in-charge since February 14, 2022.

2.    DPGC convener since July 2018.

3.   Chief Warden Diamond Hostel during July 01, 2019 - June 30, 2020.

4.   Warden Diamond Hostel during June 01, 2018 - June 30, 2019.

5.   Coordinator of M. Tech (Data Analytics) course continuously from Session 2019- 2020.

6.   JRF in-charge (Mathematics & Computing / Applied Mathematics) since September 218.

7.   Member of central library committee during June 01, 2015 - May 31, 2018.

8.   Coordinator of M. Tech (M & C) Integrated course during Session 2011-12 to June 2019.      

(II- External):

9.   Member of the Board of the school of Physical Sciences, Mizoram University, since October 2023.

Invited Talk:

  1. 90th Annual Conference of the Indian Mathematcal Society during December 23- 26, 2024 organized by Dr. Vishwanath Karad MIT World Peace University, Pune. (Delivered a talk entitled ”An operational calculus of µth order Mehler-Fock transform”)
  2. 8th Refresher Course in Mathematics for teachers of University and Colleges (RCM 2023) during December 08-21, 2023 organized by Malviya Mission Teacher Training Centre, Deen Dayal Upadhyaya Gorakhpur University, Gorakhpur. (Delivered a talk entitled ”Linear canonical transform and allied wavelet transform”)
  3. Instructional School for Mathematical Foundation (ISMF 2022) during October 08-23, 2022 organized by Indian Institute of Technology, Patna.
  4. National conference of Academy for progress of Mathematics on Recent Advances in Mathematical Analysis and Applications(NCAPM-RAMAA-2022) during May 07 - 08, 2022 organized via hybrid mode by DST-Centre for Interdisciplinary Math- ematical Sciences, Institute of Science, BHU-Varanasi (Delivered a talk entitled” The quadratic-phase Fourier transform”).
  5. 37th Annual conference of the Mathematical Society, BHU-Varanasi on Modern Mathematics and its Applications (NCMMA-2022) during January 29 - 30, 2022 organized via virtual mode by Department of Mathematics, Institute of Science, BHU-Varanasi (Delivered a talk entitled” Wavelet transforms associated with linear canonical transform”). I was chief guest in the valedictory function of this conference.
  6. International Conference on Recent Advances in Mathematics and Computational Engineering (ICRAMCE-2022) during January 06 - 07, 2022 organized via virtual mode by SSN College of Engineering, Tamil Nadu(Delivered a talk as keynote speaker on paper entitled” Continuous wavelet transform associated with lin- ear canonical transform”). I was chief guest in the inaugural function of this conference.
  7. International conference on Analysis and its Applications-2020 (ICAA   2020 Nepal), during April 9-11, 2021 organized via virtual mode jointly by Nepal Math- ematical Society, Tribhuvan University, Khamandu University, South Asian Uni- versity, New Delhi, (Delivered a talk on paper entitled” The convolution and pseudo-differential operator associated with zero-order Mehler-Fock transform”).,
  8. Short Term Training Programme on Nonlinear Analysis and its Application to Optimization Techniques during August 18 - 22, 2017 at Department of Applied Mathematics, Indian Institute of Technology (ISM), Dhanbad.
  9. QIP Short term course on Algebra, Analysis and Applications during July 03- 09, 2017 at Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi.
  10. National Conference on Applications of Mathematics during February 25-26, 2016 at Department of Mathematics and Computer Science, Mizoram University, Aizwal. (Delivered a talk on paper entitled “Differential Operator Associated with frac- tional Fourier transform”).
  11. Conference on Analysis and Applications during December 09-11, 2017 at Depart- ment of Mathematics,South Asian University, New Delhi. (Delivered a talk on paper entitled “A pair of linear canonical transformations and associated pseudo- differential operators”). 
  12. International Conference on Applied & Computational Mathematics during Octo- ber 03-06, 2012 at Institute of Applied Mathematics, Middle East Technical Uni- versity, Ankara, Turkey. (Delivered a talk on paper entitled “The fractional Fourier transform and its Applications”). 
  13. Advanced Training Programme on Integral Transforms, Wavelets, Distribution Theory and Applications during July 12-21, 2012 at DST- Centre for Interdisci- plinary Mathematical Sciences, Banaras Hindu University, Varanasi, Delivered a talk on paper entitled “The Generalized Wavelet Transform associated with Fractional Fourier Transform”).
  14. Under Graduate Training Programme in Linear Algebra and Analysis during May 28- June 06, 2012 at Department of Applied Mathematics, Indian School of Mines, Dhanbad (Delivered some lectures on Wavelets). 
  15. Workshop on Approximation Theory and Signal Analysis during March 21-24, 2009 at Institute of Biomathematics and Biometry at the Helmholtz centre Munich, Lin- dau (Lake Constance), Germany. (Delivered a talk on paper entitled “A gener- alized Pseudo-differential Operator on Gel’fand-Shilov Space and Sobolev Space”).

Conference / Symposium /Workshop Attended / Presented papers: International:

  1. 14th International Society for Analysis, its applications and Computation (ISAAC 2023) Congress, July 17-21, 2023, organized by University of S˜ao Paulo, Campus Ribeir˜ao Preto, Brazil. (Delivered a talk on paper entitled ”Pseudo-differential operator associated with index Whittaker transform”).
  2. 3rd International Conference on Subdivision; Geometric and Algebraic Methods; Isogeometric Analysis and Refinability, (SMART 2022) September 20-24, 2022, organized by University of Bologna, Italy at Rimini, Italy. (Delivered a talk on paper entitled “Weyl transform associated with linear canonical wavelets”).
  3. International Conference on Analysis and its Applications- 2021, April 08-11, 2021, organized by Nepal Mathematical Society, Kathmandu. (Delivered a talk on paper entitled “The convolution and pseudo-differential operator associated with zero-order Mehler–Fock transform”).
  4. International Conference “Strobel18” Harmonic Analysis and Applications, June 04-08, 2018, Strobl, Austria. (Delivered a Scientific talk on paper entitled “Pseudo-differential operators involving Kontorovich-Lebedev Transform”).
  5. 7th Conference on Function Spaces, May 20-24, 2014, at Southern Illinois Univer- sity, Edwardsville, USA. (Delivered a talk on paper entitled “Pseudo-differential operators involving Hankel-Clifford Transformation”).
  6. International Conference on Applied & Computational Mathematics, October 03- 06, 2012 at Institute of Applied Mathematics, Middle East Technical University, Ankara, Turkey. (Delivered a talk on paper entitled “The fractional Fourier transform and its Applications”).
  7. International Conference on Applied Mathematics & Approximation Theory, May 17-20, 2012 at TOBB University of Economics, Ankara, Turkey. (Delivered a talk on paper entitled “Boundedness of pseudo-differential operator associated with fractional Fourier transform”).
  8. International Congress of Mathematicians (ICM-2010), September 19-27, 2010, at Hyderbad Convention Centre (HICC), Organized by Univresity of Hyderabad. (Presented a Paper entitled “Continuity of Pseudo–Differential Operator Involv- ing Hankel Translation and Hankel Convolution on some Gevrey Spaces”).
  9. Workshop on Approximation Theory and Signal Analysis (March 21-24, 2009), Institute of Biomathematics and Biometry at the Helmholtz centre Munich, Lindau (Lake Constance), Germany. (Delivered a talk on paper entitled “A generalized Pseudo-differential Operator on Gel’fand-Shilov Space and Sobolev Space”).
  10. Ninth conference of the International academy of Physical Sciences (CONIAPS IX, 2007) February 3-5, 2007), Department of Mathematics, Dr. B. R. Ambedkar (Agra) University, Agra.
  11. International Conference on Analysis and Application (December; 22-25, 2003), Department of Mathematics, B.H.U. Varanasi.
  12. International Conference on Geometry, Analysis and Applications (August; 21-24, 2000), Department of Mathematics, B.H.U. Varanasi.

National:

  1. 80th Annual conference of the Indian Mathematical Society (December 27-30, 2014) at Department of Applied Mathematics, Indian School of Mines, Dhanbad (Partic- ipated)
  2. Advanced Training Programme on Integral Transforms, Wavelets, Distribution Theory and Applications (July 12-21, 2012), DST- Centre for Interdisciplinary Mathematical Sciences, Banaras Hindu University, Varanasi, Delivered a talk on paper entitled “The Generalized Wavelet Transform associated with Fractional Fourier Transform”
  3. Under Graduate Training Programme in Linear Algebra and Analysis May 28- June 06, 2012), Department of Applied Mathematics, Indian School of Mines, Dhanbad (Delivered some lectures on Wavelets).
  4. 25th Annual Conference of the Mathematical Society (December; 22-24, 2009) at Department of Mathematics B.H.U. Varanasi-5. (Presented a paper entitled “Continuity of Hankel Potential Involving Hankel Translation and Hankel Convo- lution on some Gevrey Spaces”).
  5. National seminar on Recent Advances in Theoretical and Applied Seismology (March 27-28, 2009), Department of Applied Mathematics , Indian School of Mines Uni- versity, Dhanbad-826004. (Presented a paper entitled “A generalized Pseudo- differential operator on Gel’fand-Shilov Space”)
  6. 24th Annual Conference of the Mathematical Society (December; 30-31, 2008) at Department of Mathematics B.H.U. Varanasi-5. (Presented a paper entitled “Hankel Transformation on a Gevrey Space”).
  7. 4th Group monitoring workshop cum 7th meeting of the expert panel on Fast Track Proposals for Young Scientist in Physical and Mathematical Sciences held on April 19-20, 2007 at Sikkim Manipal Institute of Technology, Sikkim.
  8. National conference on Modern Analysis and Allied Areas (February 23-24, 2007) at Department of Mathematics, B.H.U.Varanasi-5. (Presented a paper entitled “The Sobolev Type Spaces”).
  9. XXII Annual Conference of The Mathematical Society (December; 15-16, 2006) at Department of Mathematics B.H.U. Varanasi-5.
  10. The conference on Mathematics of Bharata Ganita Parisad (November;18-19, 2006)at the Department of Mathematics & Astronomy, Lucknow University Lucknow. (Pre- sented a paper entitled “The Closable; Maximal and Minimal Pseudo-differential operator”).
  11. The XVI Annual Conference of the Jammu Mathematical Society (March; 01-03, 2006) at Department of Mathematics, University of Jammu.
  12. XXI Annual Conference of The Mathematical Society (January; 23-24, 2006) at Department of Mathematics B.H.U Varanasi-5, (Presented a paper entitled “An Introduction to Pseudo- Differential Operators”).
  13. National Conference on Analysis and its Application (January; 20-22, 2006) at Department of Mathematics, B.H.U.Varanasi-5. (Presented a paper entitled “Pseudo-Differential Operator Involving Hankel Translation and Hankel Convolu- tion on some Gevrey Spaces”).
  14. National Symposium on Scientific Computing with Application to Partial Differen- tial Equations (Nov; 19-21, 2005), at Department of Mathematics, Indian Institute of Technology, Kanpur.
  15. National Conference on Emerging Areas in Mathematical Sciences in first Quarter of the Century (February; 11-13, 2005), Indian Society of Mathematics and Math- ematical Sciences at D.D.U University Gorakhpur. (Presented a paper entitled “The Generalized Pseudo-Differential Operator on some Gevrey Spaces”).
  16. National Board of Higher Mathematics, Olympiad Problem Solving Camp. (Novem- ber; 25-28, 2002), Department of Mathematics, B.H.U Varanasi.
  17. Third Annual Conference of the Society for the Special Functions and their Appli- cations (March; 4-6, 2002), Department of Mathematics, B.H.U Varanasi, (Pre- sented a paper entitled “Continuity of Pseudo-Differential Operators Associated with the Bessel Operator in some Gevrey Spaces”).

Guidance

Ph. D Guided/Supervising

* Guided (Sole): Nineteen

S.N.

Regn. No.

Name

                     Topic

Year

1.

19DR01791

R.K. Verma

Characterization of Dunkl transform and development of its associated operators

2024

2.

18DR0011

Ajay K. Gupt

Investigations and theoretical developments on the Lebedev-Skalskaya transforms

2024

3.

17DR000567

Amit Kumar (External Guide: Prof. Pankaj Jain)

Recent advances in linear canonical transform and allied operators

2022

4.

17DR000573

Manab Kundu

Linear canonical transform and its generalization in quaternion settings

2022

5.

17DR000464

J. S. Maan

A comprehensive analysis of certain operators related to the index Whittaker transform

2022

6.

2016DR000120

Sandeep. K. Verma

Characterization of zero-order Mehler-Fock transform and its allied operators

2021

7.

2015DR1000

Pratap B. Sharma

A progress on quadratic-phase Fourier transform and related operators

2021

8.

2015DR0114

Zamir A. Ansari

Study of certain integral operators in the framework of linear canonical transform domain

2020

9.

2015DR0314

Tanuj Kumar

An investigation and development of a pair of linear canonical Hankel transforms and some allied integral operators

2019

10.

2014DR0165

Upain K. Mandal

Study of Kontorovich-Lebedev transforms and related operators

2018

11.

2014DR0010

Puneet K. Maurya

An investigation and development of Hankel-type integral transformations and associated operators

2017

12.

2013DR0184

Kanailal Mahato

Study of certain pseudo-differential operators and wavelet transforms associated with fractional Hankel transforms

2017

13.

2012DR0171

Manoj K. Singh

A study of pseudo-differential operators involving Fourier-Jacobi transform and Sobolev type spaces

2016

14.

2012DR0181

Praveen Kumar

Investigation in the theory of fractional wavelet transform and pseudo-differential operator

2016

15.

2012DR0170

Sumant Kumar

Pseudo-differential operators involving Hankel-Clifford transformations and wavelet transformation

2015

16.

2012DR1008

Vanita Jain (External Guide: Prof. P. K. Jain)

Certain classes of analytic functions in the unit disk having negative coefficients

2014

17.

2010DR0001

Vishal K. Singh

Pseudo-differential operators on some function and distribution spaces

2013

18.

2009DR0021

Ashutosh Mahato

The fractional wavelet transforms on some function spaces

2013

19.

2008DR0040

Manish Kumar

A study of certain pseudodifferential operators on function and distribution spaces

2012

 Supervising: Three

S.N.

Regn. No.

Name

                                       Topic

1.

23DR0282

Pratiksha Moond

 

                                        ….

2.

23DR0129

Raj Kumar

                                         ….

3.

22DR0230

Sudhanshu Ranjan

The µ th order Mehlar-Fock transform and some

allied operators

M. Phil Supervised (Guided /Enrolled):

Guided: Five

S.N.

Regn. No.

Name

Topic

Year

1.

2014MP0016

Chandra Roy

The wavelet transformation involving first fractional Hankel transformation

2015

2.

2013MP0042

D. Biswal

Hankel-Clifford transformation and pseudo-differential operator

2014

3.

2012MP0028

Kanailal Mahato

A study on pseudo-differential operators

2013

4.

2011MP0004

Santanu Manna

A study of fractional Fourier transform and continuous wavelet transform

2012

5.

2010MP0007

B. S. Kumbhakar

An introduction to fractional Fourier transform

2011

M. Sc./M.Tech (Project/Dissertations) Guided/Enrolled:

* Two Years M. Sc (M&C):

(a) Guided: Twenty-seven

(b) Enrolled:

* Five Years Integrated M. Sc/M.Tech (M&C):

 (a) Guided: Eleven

(b) Enrolled: Two

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