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“Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. “Immortality” may be a silly word, but probably a mathematician has the best chance of whatever it may mean.” ~~G.H. Hardy, A Mathematician's Apology
Broadly speaking, my research interests lie in harmonic analysis on Lie groups and symmetric spaces. My work has primarily focused on the following themes:
Uncertainty principles and their connections with quasi-analyticity,
Maximal functions, and
Extension problems and Hardy-type inequalities.
More recently, I have also developed an interest in representation theory, with a particular focus on Harish-Chandra modules.
Publications:
Dimension-free estimates for the vector-valued Hardy--Littlewood maximal function on the Heisenberg group with Abhishek Ghosh. Journal of Functional Analysis, 2026. DOI
Weighted estimates for Hardy-Littlewood maximal functions on Harmonic NA groups with Tapendu Rana, and Jayanta Sarkar. Mathematische Zeitschrift, 2025. DOI
A note on L^p-factorizations of representations with Bernhard Kroetz and Job Kuit. Indagationes Mathematicae, 2025. DOI
Strong unique continuation for variable coefficient parabolic operators with Hardy type potential with Agnid Banerjee, and Abhishek Ghosh. Journal of Differential Equations, 2024. DOI
An extension problem, trace Hardy and Hardy's inequalities for the Ornstein-Uhlenbeck operator with Ramesh Manna, and Sundaram Thangavelu. Analysis & PDE, 2023. DOI
An analogue of Ingham's theorem on the Heisenberg group with Sayan Bagchi, Jayanta Sarkar, and Sundaram Thangavelu. Mathematische Annalen, 2023. DOI
Analogues of theorems of Chernoff and Ingham on the Heisenberg group with Sundaram Thangavelu. Journal d'Analyse Math\'ematique,149, 2023. DOI
On a theorem of Chernoff on rank one Riemannian symmetric spaces with Ramesh Manna, and Sundaram Thangavelu. Journal of Functional Analysis, 2022. DOI
An uncertainty principle for spectral projections on rank one symmetric spaces of noncompact type with Sundaram Thangavelu. Ann. Mat. Pura Appl. (AMPA), 2021. DOI
Theorems of Chernoff and Ingham for certain eigenfunction expansions with Sundaram Thangavelu. Advances in Mathematics, 2021. DOI
On the lacunary spherical maximal function on the Heisenberg group with Sundaram Thangavelu. Journal of Functional Analysis, 2021. DOI
Preprints:
On Rellich-type asymptotics for eigenfunctions on rank one symmetric spaces of noncompact type. (2025) arXiv
On norms on Harish-Chandra modules with Joseph Bernstein, Bernhard Kroetz, Job Kuit, and Eitan Sayag. (2025) arXiv
L^p- Heisenberg--Pauli--Weyl uncertainty inequalities on certain two-step nilpotent Lie groups with Jayanta Sarkar (2025) arXiv
My collaborators:
- Sayan Bagchi (IISER Kolkata)
- Agnid Banerjee (Arizona State University (ASU))
- Abhishek Ghosh (IIT Jammu)
- Bernhard Krötz (Universität Paderborn)
- Job J. Kuit (Universität Paderborn)
- Ramesh Manna (NISER Bhuwaneswar)
- Tapendu Rana (Ghent University)
- Jayanta Sarkar (IISER Kolkata)
- Sundaram Thangavelu (IISc Bangalore)
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