• Rudra P Sarkar

Articles written in Proceedings – Mathematical Sciences

• A complete analogue of Hardy’s theorem on SL2(ℝ) and characterization of the heat kernel

A theorem of Hardy characterizes the Gauss kernel (heat kernel of the Laplacian) on ℝ from estimates on the function and its Fourier transform. In this article we establisha full group version of the theorem for SL2(ℝ) which can accommodate functions with arbitraryK-types. We also consider the ‘heat equation’ of the Casimir operator, which plays the role of the Laplacian for the group. We show that despite the structural difference of the Casimir with the Laplacian on ℝn or the Laplace—Beltrami operator on the Riemannian symmetric spaces, it is possible to have a heat kernel. This heat kernel for the full group can also be characterized by Hardy-like estimates.

• Cowling-price theorem and characterization of heat kernel on symmetric spaces

We extend the uncertainty principle, the Cowling-Price theorem, on noncompact Riemannian symmetric spacesX. We establish a characterization of the heat kernel of the Laplace-Beltrami operator onX from integral estimates of the Cowling-Price type.

• On the Schwartz Space Isomorphism Theorem for Rank One Symmetric Space

In this paper we give a simpler proof of the $L^p$-Schwartz space isomorphism $(0 &lt; p\leq 2)$ under the Fourier transform for the class of functions of left 𝛿-type on a Riemannian symmetric space of rank one. Our treatment rests on Anker’s [2] proof of the corresponding result in the case of left 𝐾-invariant functions on 𝑋. Thus we give a proof which relies only on the Paley–Wiener theorem.

• Abel Transform on $PSL(2, \mathbb{R})$ and some of its Applications

We shall investigate the use of Abel transform on $PSL_2(\mathbb{R})$ as a tool beyond 𝐾-biinvariant setup, discuss its properties and show some applications.

• # Proceedings – Mathematical Sciences

Current Issue
Volume 129 | Issue 5
November 2019

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019