arXiv subjects

Rudra P Sarkar

Publications and source records attributed to Rudra P Sarkar.

6 recordsLinked to original sources

arXiv2014

Function with its Fourier transform supported on annulus and eigenfunction of Laplacian

We explore the possibilities of reaching the characterization of eigenfunction of Laplacian as a degenerate case of the inverse Paley-Wiener theorem (characterizing functions whose Fourier transform is supported on a compact annulus) for the Riemannian symmetric spaces of noncompact type. Most distinguished prototypes of these spaces are the hyperbolic spaces. The statement and the proof of the main result work mutatis-mutandis for a number of spaces including Euclidean spaces and Damek-Ricci spaces.

math.FA↗

arXiv2011

Chaotic Dynamics of the heat semigroup on the Damek-Ricci spaces

The Damek-Ricci spaces are solvable Lie groups and noncompact harmonic manifolds. The rank one Riemannian symmetric spaces of noncompact type sits inside it as a thin subclass. In this note we establish that for any Damek-Ricci space $S$, the heat semigroup generated by certain perturbation of the Laplace-Beltrami operator is {\em chaotic} on the Lorentz spaces $L^{p,q}(S)$, $2<p<\infty, 1\le q<\infty$ and subspace-chaotic on the weak $L^p$-spaces. We show that both the amount of perturbation and the range of $p$ are sharp. This generalizes a result in \cite{J-W} which proves that under identical conditions, the heat semigroup mentioned above is {\em subspace-chaotic} on the $L^p$-spaces of the symmetric spaces.

math.FA↗

arXiv2009

A note on growth of Fourier transforms and Moduli of continuity on Damek Ricci spaces

We obtain results related to boundedness of the growth of Fourier transform by the modulus of continuity on Damek-Ricci spaces. For noncompact riemannian symmetric spaces of rank one, analogues of all the results follow the same way.

math.HO↗

arXiv2007

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 $(0< p\leq 2)$ 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 \cite{A} 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.

math.RT↗

arXiv2005

Beurling's Theorem and characterization of heat kernel for Riemannian Symmetric spaces of noncompact type

We prove Beurling's theorem for rank 1 Riemmanian symmetric spaces and relate it to the characterization of the heat kernel of the symmetric space.

math.FA↗

arXiv2004

Cowling-Price theorem and characterization of heat kernel on symmetric spaces

We extend the uncertainty principle, the Cowling--Price theorem, on non-compact Riemannian symmetric spaces $X$. We establish a characterization of the heat kernel of the Laplace--Beltrami operator on $X$ from integral estimates of the Cowling--Price type.

math.RT↗