On the Schwartz space isomorphism theorem for rank one symmetric space

Details On the Schwartz space isomorphism theorem for rank one symmetric space On the Schwartz space isomorphism theorem for rank one symmetric space

2007-09-21

arxiv.org/abs/0709.3343v1

Mathematics

Representation Theory

16 pages

Scientific paper

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 $\delta$-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.

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