arXiv subjects

Joydip Jana

Publications and source records attributed to Joydip Jana.

3 recordsLinked to original sources

arXiv2010

On the Schwartz space isomorphism theorem for the Riemannian symmetric spaces

We deduce a proof of the isomorphism theorem for certain closed subspace $\mc S^p_Γ(X)$ of the $L^p$-Schwartz class functions $(0< p \leq 2) $ on a Riemannian symmetric space $X$ where $Γ$ is a finite subset of $\what{K}_M$. The Fourier transform considered is the Helgason Fourier transform. Our proof relies only on the Paley-Wiener theorem for the corresponding class of functions and hence it does not use the complicated higher asymptotics of the elementary spherical functions.

math.RT↗

arXiv2009

Image of Schwartz Space Under Spectral Projection

Let $X= G/K$ symmetric space of non compact type, where $G$ is a rank-one connected semisimple Lie group with finite center. We shall look at the transform $ P_λf(x) = f \ast φ_λ(x)$, where, $λ\in \mathbb C$ and $φ_λ$ is the elementary spherical function. We shall try to characterizes the image of the Schwartz spaces $S^p(X) $ where $0 < p \leq 2$ under the above transform.

math.RT↗

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↗