Proceedings Mathematical Sciences

, Volume 117, Issue 3, pp 333–348

On the Schwartz space isomorphism theorem for rank one symmetric space

Article

DOI: 10.1007/s12044-007-0029-6

Cite this article as:
Jana, J. & Sarkar, R.P. Proc Math Sci (2007) 117: 333. doi:10.1007/s12044-007-0029-6

Abstract

In this paper we give a simpler proof of the Lp-Schwartz space isomorphism (0 < p ≤ 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.

Keywords

δ Spherical transform Helgason Fourier transform 

Copyright information

© Indian Academy of Sciences 2007

Authors and Affiliations

  1. 1.Indian Statistical InstituteDivision of Theoretical Statistics and MathematicsKolkataIndia

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