On the Schwartz space isomorphism theorem for rank one symmetric space

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/138487In 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.16 pagesRepresentation Theory22E30, 43A85On the Schwartz space isomorphism theorem for rank one symmetric spacetext