I am a Postdoctoral Researcher at the Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University. I am a member of research group “Analysis and PDEs” of Prof. Michael Ruzhansky. I completed my Ph.D. from Department of Mathematics, IIT Delhi, India under the supervisor of Prof. Ritumoni Sarma and Prof. N. Shravan Kumar. Before joining to Ghent University, I was Postdoctoral Fellow at the School of Mathematical Sciences, NISER Bhubaneswar, India.
I work in the area of Mathematical Analysis. More specifically, my interest focused on, but not limited to, harmonic analysis on locally compact groups/hypergroups/homogeneous spaces and pseudo-differential operators.
Address: Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University
Krijgslaan 281, Building S8
B 9000 Ghent, Belgium
The list of my publications:
1. Aparajita Dasgupta and Vishvesh Kumar, Ellipticity and Fredholmness of pseudo-differential operators on Zn, (submitted). arXiv link: https://arxiv.org/abs/1910.05582
2. Aparajita Dasgupta and Vishvesh Kumar, Hilbert-Schmidt and trace class pseudo-differential operators on the abstract Heisenberg group, (submitted). arXiv link: https://arxiv.org/abs/1902.09869
3. Duvan Cardona and Vishvesh Kumar, The nuclear trace of periodic pseudo-differential operators with applications to index theory, (submitted). arXiv link: https://arxiv.org/abs/1901.10010
4. Vishvesh Kumar, Orlicz Modules over coset spaces of Compact subgroups in locally compact groups, (Submitted). arXiv link: https://arxiv.org/abs/1905.05971
5. Ibrahim Akbarbaglu, M. R. Azimi and Vishvesh Kumar, Topological transitive sequence of cosine operators on Orlicz spaces, (submitted). arXiv link: https://arxiv.org/abs/1809.06085
6. Vishvesh Kumar, Orlicz spaces and amenability of hypergroups, Bull. Ira. Math. Soc. (2019). DOI: https://doi.org/10.1007/s41980-019-00310-7
7. Vishvesh Kumar and Ritumoni Sarma, Hausdorff-Young inequality for Orlicz spaces on compact hypergroups, (to appear in) Colloquium Mathematicum, (2019).
8. Vishvesh Kumar and N. Shravan Kumar, Vector-valued Fourier analysis on hypergroups, (to appear in) Operator and Matrices (2019).
9. Vishvesh Kumar, Shravan Kumar, and Ritumoni Sarma, Unbounded translation invariant operators on commutative hypergroups, (to appear in) Methods of Functional analysis and Topology, (2019).
10. Vishvesh Kumar, Shravan Kumar, and Ritumoni Sarma, Characterization of multipliers on hypergroups, (to appear in) Acta Mathematica Vietnamica, (2019).
11. Duvan Cardona and Vishvesh Kumar, L^p-boundedness and L^p-nuclearity of multilinear pseudo-differential operators on Z^nand the torus T^n , Journal of Fourier analysis and applications (2019) DOI: 10.1007/s00041-019-09689-7
12. Vishvesh Kumar and M. W. Wong, C*-algebra, H*-algebra and trace ideals of pseudo-differential operators on locally compact, Hausdorff and abelian groups, Journal of Pseudo differential operators and applications, 10(2) 269-283 (2019).
13. Vishvesh Kumar, Pseudo-differential operators on homogeneous spaces of compact and Hausdorff groups, Forum Mathematicum, 31(2) 275-282 (2019).
14. Vishvesh Kumar, Kenneth A. Ross, and Ajit Iqbal Singh, Hypergroup deformations of semigroups, Semigroup Forum, 99(1) 169-195 (2019).
15. Vishvesh Kumar, Kenneth A. Ross, and Ajit Iqbal Singh, An addendum to “Hypergroup deformations of semigroups,” Semigroup Forum, 99(1) 196-197 (2019).
16. Vishvesh Kumar, Kenneth A. Ross, and Ajit Iqbal Singh, Ramsey theory for hypergroups, Semigroup Forum,(2019). DOI: https://doi.org/10.1007/s00233-019-10009-
17. Vishvesh Kumar, R. Sarma, and N. Shravan Kumar, Orlicz spaces on hypergroups, Publications MathematicaeDebrecen, 94(1-2) 31–47 (2019).
18. R. Sarma, N. Shravan Kumar, and Vishvesh Kumar, Multipliers on Vector-valued -spaces for Hypergroups, Acta Math. Sin. (Engl. Ser.) 34(7) 1059-1073 (2018).
19. Duvan Cardona and Vishvesh Kumar, Multilinear analysis for discrete and periodic pseudo-differential operators in -spaces, Rev. Integr. temas Mat, 36(2) 151-164 (2018).
20. Vishvesh Kumar, R. Sarma, and N. Shravan Kumar, Orlicz Algebras on Homogeneous Spaces of Compact Groups and Their Abstract Linear Representations, Mediterr. J. Math. 15(4), Art 186, 13pp. (2018).