Research

So far, I mainly worked in the field of harmonic analysis, with a focus on Restriction problems and Strichartz estimates, Pseudo-differential operators, Analysis of PDEs, and Time-frequency analysis.

Pseudo-differential operators:

1. A. Dasgupta, L. Mohan, and S. S. Mondal, Weighted periodic and discrete pseudo-differential operators, Monatsh. Math. (2024). https://doi.org/10.1007/s00605-024-01976-w 

2.  A. Dasgupta, L. Mohan, and S. S. Mondal, Multilinear Fourier integral operators on modulation spaces, Forum Math. (2023) https://doi.org/10.1515/forum-2023-0158 

3.  V. Kumar and S. S. Mondal, Symbolic calculus and $M$-elliptic pseudo-differential operators on $\ell^2( \mathbb{Z}^n)$, Analysis and Applications (Anal. Appl.) (2023).  https://doi.org/10.1142/S0219530523500215

4. V. Kumar and S. S. Mondal, Trace class and Hilbert-Schmidt pseudo differential operators on the Heisenberg motion group, Appl. Anal. (2022).   https://doi.org/10.1080/00036811.2022.2078717 

5. A. Maity and S. S. Mondal,  A note on Singular integral,  Analysis (2023). https://doi.org/10.1515/anly-2022-1107 

6.  S. S. Mondal, Boundedness and nuclearity of pseudo-differential operators on homogeneous trees, Anal. Math. Phys. (2022).  https://doi.org/10.1007/s13324-022-00691-9 

7.  V. Kumar and S. S. Mondal,  Schatten class and nuclear pseudo-differential operators on homogeneous spaces of compact groups,  Monatsh. Math. (2021).  https://doi.org/10.1007/s00605-021-01663-0 

8.  S. S. Mondal,  Characterizations of self-adjointness, normality of pseudo differential operators on homogeneous space of compact group,  Complex Var. Elliptic Equ. (2021).  https://doi.org/10.1080/17476933.2021.1913131 

9.  V. Kumar and S. S. Mondal, Trace class and Hilbert-Schmidt pseudo differential operators on step two nilpotent Lie groups,  Bull. Sci. Math. (2021).  https://doi.org/10.1016/j.bulsci.2021.103015 

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

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

12. A. Dasgupta, V. Kumar, L. Mohan, and S. S. Mondal, Non-harmonic $M$-elliptic pseudo-differential operators on manifolds with  boundary, (2023). https://arxiv.org/abs/2307.1082

13.  A. Dasgupta, L. Mohan, and S. S. Mondal, Weighted periodic and discrete pseudo-differential operators, (2022).  https://arxiv.org/abs/2208.10141

14. V. Kumar and  S. S. Mondal,  Szego Limit theorem for Anharmonic Oscillators (Submitted).

Strichartz Inequalities and Restriction Problems:

1.  S. S. Mondal and  M. Song, Orthonormal Strichartz inequalities for the $(k,a)$-generalized Laguerre operator and Dunkl operator,  Israel J. Math. (2023).  https://arxiv.org/abs/2208.12015 

2. P Jitendra K. Senapati, Pradeep B., S. S. Mondal, and H. Mejjaoli, Restriction theorems for Fourier-Dunkl transform II: Paraboloid, sphere and hyperboloid surfaces,  J. Geom. Anal. (2023).   https://doi.org/10.1007/s12220-023-01530-4 

3. S.  Ghosh, S. S. Mondal, and J.  Swain, On local dispersive and Strichartz estimates for the Grushin operator,  New York J. Math. (2024) https://arxiv.org/abs/2306.10298 

4. S. Ghosh, S. S. Mondal, and J. Swain,  Strichartz Inequality for orthonormal functions associated with special Hermite operator, Forum Math. (2023). https://doi.org/10.1515/forum-2023-0115 

5. P Jitendra K. Senapati,  Pradeep B., S. S. Mondal, and H. Mejjaoli, Restriction theorems for Fourier-Dunkl transform I: Cone surface,  J. Pseudo-Differ. Oper. Appl. (2023).  https://doi.org/10.1007/s11868-022-00499-y 

6. S. S. Mondal and J. Swain,  Restriction theorem for the Fourier-Hermite transform and solution of the Hermite-Schr\"odinger equation,  Adv. Oper. Theory  (2022).  https://doi.org/10.1007/s43036-022-00208-y 

7. S.  Ghosh, S. S. Mondal, and J.  Swain, On local dispersive and Strichartz estimates for the Grushin operator, (2023) https://arxiv.org/abs/2306.10298 

8. C. Luo, S. S. Mondal, and  M. Song, Decay estimates for a class of Dunkl wave equations, (2024)  https://arxiv.org/abs/2407.06949 

9.  G. Feng, S. S. Mondal, M. Song, and H.  Wu,  Orthonormal Strichartz estimates and their applications on abstract measure spaces, (2024) https://arxiv.org/abs/2409.14044 

10. G. Feng, S. S. Mondal, M. Song, and H.  Wu, Orthonormal Strichartz estimates for Dunkl-Schrödinger equation of initial data with Soboloev regularity, (2025) https://arxiv.org/abs/2506.05493

11. V. Kumar and  S. S. Mondal, I. Sitiraju, M. Song, Strichartz estimates for higher order Schrödinger equations with Partial regular initial data,  https://doi.org/10.48550/arXiv.2508.15670 

Analysis of PDEs:

1.  A. Dasgupta, L. Mohan, and S. S. Mondal,   Non-harmonic analysis of the wave equation for Schrödinger operators with complex potential, Discrete Contin. Dyn. Syst. (2025) https://arxiv.org/abs/2409.03027 

2. V. 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. (2025) https://arxiv.org/abs/2408.05598 

3. A. Dasgupta, S. S. Mondal, M. Ruzhansky, and A. Tushir, General Caputo-type fractional discrete diffusion equation for Schr\"{o}dinger operator,  Fract. Calc. Appl. Anal (2024). https://arxiv.org/abs/2402.13690  

4. A. Dasgupta, V. 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 

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

6.  A. Dasgupta, V. Kumar, and S. S. Mondal,  Nonlinear fractional damped wave equation on compact Lie groups, Asymptot. Anal. (2023).  https://doi.org/10.3233/ASY-231842 

7. A. Dasgupta, V. Kumar, and S. S. Mondal,  Nonlinear fractional wave equation on compact Lie groups, (2022). https://arxiv.org/abs/2207.04422 

8. A. Dasgupta, S. S. Mondal, M. Ruzhansky, and A. Tushir, A. Tushir, Discrete time-dependent wave equation for the Schr\"{o}dinger operator with unbounded potential,  (2023). http://arxiv.org/abs/2306.02409 

9. A. Dasgupta, V. 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://arxiv.org/abs/2404.08766 (2024).  

10. A. Dasgupta, S. S. Mondal and A. Tushir,  Fractional semilinear damped wave equation on the Heisenberg group, (2025). https://arxiv.org/abs/2501.10816 .

Time frequency Analysis:

1.  S. S. Mondal and A. Poria,  Weighted norm inequalities for the Opdam Cherednik transform, Internat. J. Math. (2022). https://doi.org/10.1142/S0129167X22500665 

2. S. S. Mondal and A. Poria, Qualitative uncertainty principles for the windowed Opdam--Cherednik transform on weighted modulation spaces,  Math. Methods Appl. Sci. (2022).  https://doi.org/10.1002/mma.8376 

3.  S. S. Mondal and A. Poria, Hausdorff operators associated with the Opdam Cherednik transform in Lebesgue spaces, J. Pseudo-Differ. Oper. Appl. (2022).  https://doi.org/10.1007/s11868-022-00462-x 

4. Pradeep B., H. Mejjaoli, S. S. Mondal, and  P Jitendra K. Senapati,  Time-frequency analysis of $(k,a)$-generalized wavelet transform and applications,  J. Math. Phys. (2023). https://doi.org/10.1063/5.0152806 

5. S. S. Mondal and A. Poria,  Uncertainty principles for the windowed Opdam Cherednik transform, Math. Methods Appl. Sci. (2023). https://doi.org/10.1002/mma.9596