Books Edited:

1. V. Kumar, D. Rottensteiner, M. Ruzhansky (Eds.) Pseudo-Differential Operators and Related Topics. Extended Abstracts PSORT 2024, Research Perspectives Ghent Analysis and PDE Center, Trends in Mathematics, Birkhäuser, 2025. x+174pp. link

👉  The preprint version of a paper may differ from the published version.

Geometric Analysis and PDEs:

Preprints:

1. S. Bhowmick, S. Ghosh and Vishvesh Kumar, Infinitely many solutions for nonlinear superposition operators of mixed fractional order involving critical exponent. https://doi.org/10.48550/arXiv.2506.11832 

2. Y. Aikyn, S. Ghosh, Vishvesh Kumar and M. Ruzhansky, Brezis-Nirenberg type problems associated with nonlinear superposition operators of mixed fractional order. https://doi.org/10.48550/arXiv.2504.05105 

3. Vishvesh Kumar and B. T. Torebek, Fujita-type results for the semilinear heat equations driven by mixed local-nonlocal operators. https://doi.org/10.48550/arXiv.2502.21273 

4. S. Ghosh and Vishvesh Kumar, Critical equations involving nonlocal subelliptic operators on stratified Lie groups: Spectrum, bifurcation and multiplicity. https://doi.org/10.48550/arXiv.2501.12791 

5. S. Ghosh, T. Gou, Vishvesh Kumar and V. D. Rădulescu, Fractional Morrey-Sobolev type embeddings and nonlocal subelliptic problems with oscillating nonlinearities on stratified Lie groups. Submitted.

6. S. Ghosh and Vishvesh Kumar, Nonlocal subelliptic systems involving concave-convex nonlinearities on stratified Lie groups. Submitted.

7. S. Ghosh, Vishvesh Kumar and M. Ruzhansky, Subelliptic nonlocal Brezis-Nirenberg problems on stratified Lie groups. https://doi.org/10.48550/arXiv.2409.03867 

8. A. Dasgupta, Vishvesh Kumar, S. S. Mondal and M. Ruzhansky, Higher order hypoelliptic damped wave equations on graded Lie groups with data from negative order Sobolev spaces. https://doi.org/10.48550/arXiv.2404.08766 

9. S. Ghosh, Vishvesh Kumar and M. Ruzhansky, Best constants in subelliptic fractional  Sobolev and Gagliardo-Nirenberg inequalities and ground states on stratified Lie groups. https://doi.org/10.48550/arXiv.2306.07657 

Papers:

1. Vishvesh Kumar, S. S. Mondal, M. Ruzhansky and B. Torebek, Higher order hypoelliptic damped wave equations on graded Lie groups with data from negative order Sobolev spaces:  the critical case.   J. Evol. Equ.  25(58), (2025). https://doi.org/10.1007/s00028-025-01082-w  Preprint version: https://doi.org/10.48550/arXiv.2408.05598 

2. R. Zhang, Vishvesh Kumar and M. Ruzhansky, Liouville-type theorem for higher order Hardy-Hènon type systems on the sphere,  J. Math. Anal. Appl. 543(2) (2025) 129029. https://doi.org/10.1016/j.jmaa.2024.129029 

3. Vishvesh Kumar, M. Ruzhansky and R. Zhang, Liouville type theorems for subelliptic systems on the Heisenberg group with general nonlinearity, Ann. Fenn. Math. 49(2), (2024). https://doi.org/10.54330/afm.148660       Preprint Version: https://doi.org/10.48550/arXiv.2303.04210  

4. A. Dasgupta, Vishvesh Kumar, S. S. Mondal and M. Ruzhansky, Semilinear damped wave equations on the Heisenberg group with initial data from Sobolev spaces of negative order,  J. Evol. Equ. 24(51),  (2024). https://doi.org/10.1007/s00028-024-00976-5 (Open Access).

5. A. K. Bhardwaj, Vishvesh Kumar and S. S. Mondal, Estimates for the nonlinear viscoelastic damped wave equation on compact Lie groups. Proc. Roy. Soc. Edinburgh Sect. A.  154(3) , (2024) 810 - 829. https://doi.org/10.1017/prm.2023.38  Preprint Version: https://doi.org/10.48550/arXiv.2207.06645

6. R. Zhang, Vishvesh Kumar and M. Ruzhansky, A Direct Method of Moving Planes for Logarithmic Schrödinger Operator,  Z. Anal. Anwend.  43(3/4) (2024) 287-297.  https://doi.org/10.4171/zaa/1757   (Open Access)    

7. S. Ghosh, Vishvesh Kumar and M. Ruzhansky, Compact Embeddings, Eigenvalue Problems, and subelliptic Brezis-Nirenberg equations involving singularity on stratified Lie groups, Math. Ann. 388, (2024) 4201–4249.  https://doi.org/10.1007/s00208-023-02609-7  (Open Access).  

8. R. Zhang, Vishvesh Kumar and M. Ruzhansky, Symmetry of positive solutions for Lane-Emden systems involving the Logarithmic Laplacian, Acta Appl. Math.188, 16 (2023). https://doi.org/10.1007/s10440-023-00627-w.  Preprint Version: https://doi.org/10.48550/arXiv.2210.09110 

9. A. Dasgupta, Vishvesh Kumar and S. S. Mondal, Nonlinear fractional dumped wave equations on compact Lie groups, Asymptot. Anal. 134 (3-4), (2023)  485-511. https://doi.org/10.3233/ASY-231842   Preprint Version:  https://doi.org/10.48550/arXiv.2211.06155 

(Abstract) Harmonic analysis:

Preprints:

1. Vishvesh Kumar, T. Rana and M. Ruzhansky, Classical inequalities for all Fourier matrix coefficients of SL(2, R) and their applications.  https://doi.org/10.48550/arXiv.2409.17918  

2. Vishvesh Kumar, M. Ruzhansky and H.-W. Zhang, Stein-Weiss inequality on non-compact symmetric spaces. https://doi.org/10.48550/arXiv.2310.19412 

3. Vishvesh Kumar, M. Ruzhansky and H.-W. Zhang, Smoothing properties of dispersive equations on non-compact symmetric spaces. https://doi.org/10.48550/arXiv.2302.03961 

Papers: 

1. Vishvesh Kumar, $Lp$-L^q$ hypergeometric spectral and Fourier multipliers associated with root systems, Potential Anal.  (2025). https://doi.org/10.1007/s11118-025-10213-4 

2. M. Kumar, Vishvesh Kumar and M. Ruzhansky, Titchmarsh theorems on Damek-Ricci spaces via moduli of continuity of higher order, Internat. J. Math.  (2025).  https://doi.org/10.1142/S0129167X25500016  Preprint version: https://doi.org/10.48550/arXiv.2205.06028 

3. A. Kassymov, Vishvesh Kumar and M. Ruzhansky,  Functional inequalities on symmetric spaces of noncompact type and applications,  J. Geom. Anal.  34( 208),  (2024). https://doi.org/10.1007/s12220-024-01644-3 (Open access) Preprint version:  https://doi.org/10.48550/arXiv.2212.02641 

4. Vishvesh Kumar,  J. E. Restrepo and  M. Ruzhansky,  Asymptotic estimates for the growth of Deformed Hankel transform by modulus of continuity, Results Math. 79(22), (2024). https://doi.org/10.1007/s00025-023-02051-w    

5. Vishvesh Kumar and M. Ruzhansky, $L^p$-$L^q$ multipliers on commutative hypergroups, J. Aust. Math. Soc. 115(3),  (2023), 375-395.  https://doi.org/10.1017/S1446788723000125 

6. Vishvesh Kumar and M. Ruzhansky, $L^p$-$L^q$ boundedness of (k, a)-Fourier multipliers with applications to nonlinear equations,  Int. Math. Res. Not. IMRN, no. 2, (2023) 1073-1093.  10.1093/imrn/rnab256  (Open Access).    

7. Vishvesh Kumar and M. Ruzhansky, Hardy-Littlewood inequality and $L^p$-$L^q$ Fourier multipliers on compact hypergroups,  J. Lie theory 32(2) (2022), 475-498.  https://www.heldermann.de/JLT/JLT32/JLT322/jlt32023.htm  Preprint version: https://arxiv.org/abs/2005.08464

8. A.R. Bagheri Salec, Vishvesh Kumar and S. M. Tabatabaie, Convolution Properties of Orlicz Spaces on hypergroups,  Proc. Amer. Math. Soc. 150 (2022), 1685-1696.  DOI: https://doi.org/10.1090/proc/15799   https://arxiv.org/abs/2101.07366

9. Vishvesh Kumar and S. M. Tabatabaie, Hypercyclic Sequences of weighted translations on hypergroups, Semigroup Forum, 103, (2021), 916–934. DOI:https://doi.org/10.1007/s00233-021-10226-6  Preprint version: https://arxiv.org/abs/2003.10036 

10. Vishvesh Kumar and M. Ruzhansky, A note on K-functional, Modulus of smoothness, Jackson theorem and Bernstein-Nikolskii-Stechkin inequality on Damek-Ricci spaces, J. Approx. Theory, 264, (2021), 105537. DOI:  https://doi.org/10.1016/j.jat.2020.105537  (Preprint version: https://arxiv.org/abs/2005.01413)

11. I. Akbarbaglu, M. R. Azimi, Vishvesh Kumar, Topological transitive sequence of cosine operators on Orlicz space, Ann. Funct. Anal., 12(2), (2021).  https://doi.org/10.1007/s43034-020-00088-4   https://arxiv.org/abs/1809.06085  

12.  Vishvesh Kumar and R. Sarma, Continuity of operators intertwining with translation operators on hypergroups. Aequat. Math. 95, (2021), 343-349.  https://doi.org/10.1007/s00010-020-00745-y 

13. Vishvesh Kumar, N. Shravan Kumar and R. Sarma, Characterization of Multipliers on Hypergroups. Acta Math Vietnam 45, 783–794 (2020). https://doi.org/10.1007/s40306-020-00379-x 

14. Vishvesh Kumar and M. Ruzhansky, Hausdorff-Young inequality for Orlicz spaces on compact homogeneous manifolds, Indag. Math. (N.S.) 31(2) (2020), 266-276 https://doi.org/10.1016/j.indag.2020.01.004 

15.  Vishvesh Kumar, Kenneth A. Ross and  Ajit Iqbal Singh, Ramsey theory for hypergroups, Semigroup Forum, 100, 482–504 (2020). https://doi.org/10.1007/s00233-019-10009-0 

16.  Vishvesh Kumar, Orlicz Spaces and Amenability of Hypergroups, Bull. Iran. Math. Soc. (2019). https://doi.org/10.1007/s41980-019-00310-7 

17. Vishvesh Kumar and R. Sarma, The Hausdorff–Young inequality for Orlicz spaces on compact hypergroups, Colloq. Math. 160(1) (2020), 41-51. https://doi.org/10.4064/cm7627-4-2019 

18. Vishvesh Kumar and N. Shravan Kumar, Vector valued Fourier analysis on hypergroups, Oper. Matrices, 13(4) (2019), 1147-1161. http://oam.ele-math.com/13-76/Vector-valued-Fourier-analysis-on-hypergroups 

19. Vishvesh Kumar, N. Shravan Kumar and R. Sarma, Unbounded translation invariant operators on commutative hypergroups, Methods Funct. Anal. Topology 25(3) (2019), 236-247. http://mfat.imath.kiev.ua/article/?id=1209 

20. Vishvesh Kumar, Kenneth A. Ross and  Ajit Iqbal Singh, Hypergroup deformations of semigroups, Semigroup Forum 99(1) (2019), 169-195. https://doi.org/10.1007/s00233-019-10003-6  (An Addendum: https://doi.org/10.1007/s00233-019-10023-2 ).

21. Vishvesh Kumar, N. Shravan Kumar and R. Sarma, Orlicz spaces on hypergroups, Publ. Math. Debrecen 94(1-2) (2019), 31-47. http://publi.math.unideb.hu/load_pdf.php?p=2279 

22. Vishvesh Kumar, N. Shravan Kumar and R. Sarma, Orlicz algebras on homogeneous spaces of compact groups and their abstract linear representations, Mediterr. J. Math. 15(4) (2018), Paper No. 186, 13 pp. https://doi.org/10.1007/s00009-018-1225-6  

23.  R. Sarma, N. Shravan Kumar and Vishvesh Kumar, Multipliers on vector-valued L1-spaces for hypergroups, Acta Math. Sin. (Engl. Ser.) 34(7) (2018), 1059-1073. https://doi.org/10.1007/s10114-018-7303-7  

Pseudo-differential operators:

Preprints:

1. Vishvesh Kumar and S. S. Mondal, Szegö limit theorems for anharmonic oscillators. Submitted.

2. D. Cardona, Vishvesh Kumar and M. Ruzhansky, Pseudo-differential operators on Homogeneous vector bundles over compact homogeneous manifolds. https://doi.org/10.48550/arXiv.2403.08990 

3. D. Cardona, M. Chatzakou,  J. Delgado, Vishvesh Kumar and M. Ruzhansky, Anharmonic semigroups and applications to global well-posedness of nonlinear heat equations. https://arxiv.org/abs/2401.13750 

4. A. Dasgupta, Vishvesh Kumar, L. Mohan and S. S. Mondal, Non-harmonic M-elliptic pseudo differential operators on manifolds. https://doi.org/10.48550/arXiv.2307.10825 

Papers: 

1. D. Cardona, Vishvesh Kumar, M. Ruzhansky and N. Tokmagambetov, L^p-L^q boundedness of pseudo-differential operators on smooth manifolds and its applications to nonlinear equations, to appear in Ann. Funct. Anal. (2025). Preprint version:  https://arxiv.org/abs/2005.04936 

2. D. Cardona, Vishvesh Kumar and M. Ruzhansky, L^p-L^q boundedness of pseudo-differential operators on graded Lie groups,  New York J. Math.,  31 (2025), 722-748. https://www.emis.de/journals/NYJM/j/2025/Vol31.html   Preprint version: https://doi.org/10.48550/arXiv.2307.16094 

3. D. Cardona, Vishvesh Kumar, M. Ruzhansky and N. Tokmagambetov, Expansion of traces and Dixmier traceability  for global pseudo-differential operators on manifolds with boundary, Adv, Oper. Theory,  10(53), (2025). https://doi.org/10.1007/s43036-025-00438-w 

4. D. Cardona,  J. Delgado, Vishvesh Kumar and M. Ruzhansky, L^p-L^q estimates for subelliptic pseudo-differential operators on compact Lie groups, to appear in Osaka J. Math.  (2025) Preprint version: https://doi.org/10.48550/arXiv.2310.16247 

5. M. Chatzakou and Vishvesh Kumar, L^p-L^q boundedness of Fourier multipliers associated with the anharmonic Oscillator, J. Fourier Anal. Appl, 29(73), (2023). https://doi.org/10.1007/s00041-023-10047-x  Preprint version: https://arxiv.org/abs/2004.07801 

6. Vishvesh Kumar and S. S. Mondal, Symbolic calculus and  $M$-ellipticity of pseudo-differential operators on  Z^n,  Anal. Appl. (Singap.), 21(06),  (2023), 1447-1475. https://doi.org/10.1142/S0219530523500215  Preprint version: https://arxiv.org/abs/2111.10224 

7. D. Cardona, Vishvesh Kumar, M. Ruzhansky and N. Tokmagambetov, Global functional calculus, lower/upper bounds and evolution equations on manifolds with boundary, Adv, Oper. Theory, 8(50), (2023). https://doi.org/10.1007/s43036-023-00254-0  (Open access).  https://arxiv.org/abs/2101.02519 

8. Vishvesh Kumar and S. S. Mondal, $L^2-L^p$ estimates and  Hilbert--Schmidt  pseudo differential operators on Heisenberg motion groups, Appl. Anal. (2022). https://doi.org/10.1080/00036811.2022.2078717  

9. Vishvesh Kumar and S. S. Mondal, Schatten class and nuclear pseudo-differential operators on homogeneous spaces of compact groups, Monatsh. Math. 197 (2022), no. 1, 149–176.  DOI https://doi.org/10.1007/s00605-021-01663-0  https://arxiv.org/abs/1911.10554

10. M. Chatzakou and Vishvesh Kumar, L^p-L^q boundedness of spectral multipliers of the anharmonic oscillator, C. R. Math. Acad. Sci. Paris, 360 (2022),  343-347. https://doi.org/10.5802/crmath.290  https://arxiv.org/abs/2110.15294 

11. A. Dasgupta and Vishvesh Kumar, Ellipticity and Fredholmness of pseudo-differential operators on l^2(Z^n),  Proc. Amer. Math. Soc.  150 (7),  (2022), 2849–2860. 10.1090/proc/15661  

12. Vishvesh Kumar and S. S. Mondal, Trace class and Hilbert-Schmidt pseudo differential operators on step two nilpotent Lie groups, Bulletin des Sciences Mathématiques,171, (2021), 103015. https://doi.org/10.1016/j.bulsci.2021.103015 

13. Vishvesh Kumar and S. S. Mondal, Self-adjointness and compactness of operators related to finite measure spaces, Complex Anal. Oper. Theory, 15( 22) (2021). https://doi.org/10.1007/s11785-020-01067-2 

14. D. Cardona and Vishvesh Kumar, The nuclear trace of periodic vector-valued pseudo-differential operators with applications to index theory, Math. Nach, 294(9), (2021), 1657-1683. https://doi.org/10.1002/mana.201900040 Preprint: https://arxiv.org/abs/1901.10010 

15. Vishvesh Kumar and S. S. Mondal, Nuclearity of operators related to finite measure spaces, J. Pseudo-Differ. Oper. Appl. 11, (2020), 1031–1058. https://doi.org/10.1007/s11868-020-00353-z 

16. D. Cardona, C. del Corral and  Vishvesh Kumar, Dixmier traces for discrete pseudo-differential operators, J. Pseudo-Differ. Oper. Appl. 11, 647-656 (2020). https://doi.org/10.1007/s11868-020-00335-1 

17. A. Dasgupta and Vishvesh Kumar, Hilbert-Schmidt and Trace class pseudo-differential operators on the abstract Heisenberg group, J. Math. Anal. Appl. 486(2) (2020), 123936. https://doi.org/10.1016/j.jmaa.2020.123936  

18. D. Cardona and Vishvesh Kumar, L^p-boundedness and L^p-nuclearity of multilinear pseudo-differential operators on Z^n and the torusT^n, J. Fourier Anal. Appl. 25(6) (2019), 2973-3017. https://doi.org/10.1007/s00041-019-09689-7 

19. Vishvesh Kumar and M. W. Wong, C^∗-algebras, H^∗-algebras and trace ideals of pseudo-differential operators on locally compact, Hausdorff and abelian groups, J. Pseudo-Differ. Oper. Appl. 10(2) (2019), 269-283. https://doi.org/10.1007/s11868-019-00280-8  (Correction: https://doi.org/10.1007/s11868-020-00338-y ).

20. Vishvesh Kumar, Pseudo-differential operators on homogeneous spaces of compact and Hausdorff groups, Forum Math. 31(2) (2019), 275-282. https://doi.org/10.1515/forum-2018-0155 

21. D. Cardona and Vishvesh Kumar, Multilinear analysis for discrete and periodic pseudo-differential operators in Lp-spaces, Rev. Integr. Temas Mat. 36(2) (2018), 151-164. https://revistas.uis.edu.co/index.php/revistaintegracion/article/view/9120/8966