• On the Schwartz Space Isomorphism Theorem for Rank One Symmetric Space

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      https://www.ias.ac.in/article/fulltext/pmsc/117/03/0333-0348

    • Keywords

       

      𝛿 Spherical transform; Helgason Fourier transform.

    • Abstract

       

      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 [2] 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.

    • Author Affiliations

       

      Joydip Jana1 Rudra P Sarkar1

      1. Indian Statistical Institute, Division of Theoretical Statistics and Mathematics, 203 B.T. Road, Kolkata 700 108, India
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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