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arXiv · 1002.4855

On the Schwartz space isomorphism theorem for the Riemannian symmetric spaces

Joydip Jana
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Abstract

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.

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Joydip Jana. 2010-02-25. On the Schwartz space isomorphism theorem for the Riemannian symmetric spaces. https://arxiv.org/abs/1002.4855

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