On an analogue of the Wiener-Tauberian theorem for symmetric spaces of the noncompact type
type: Item
instance of: scholarly article
title: On an analogue of the Wiener-Tauberian theorem for symmetric spaces of the noncompact type
zbMATH Open document ID: 0628.43011
author: Alladi Sitaram
published in: Pacific Journal of Mathematics
publication date: 1988-01-01T00:00:00Z
review text: Let X be a symmetric space of the non-compact type and G the connected component of the group of isometries of X. Let K be a fixed maximal compact subgroup of G. Let f be a (left) K-finite integrable function on X. We consider conditions under which \(Sp=\{^ gf:\) \(g\in G\}\) is dense in \(L^ 1(X)\), in terms of the ``Fourier transform'' of f. This continues earlier work on this kind of problem by L. Ehrenpreis and F. I. Mautner, R. Krier and also by the author.
Mathematics Subject Classification ID: 43A85
Mathematics Subject Classification ID: 22E30
Mathematics Subject Classification ID: 53C35
zbMATH DE Number: 4021849
zbMATH Keywords: symmetric space
zbMATH Keywords: non-compact type
zbMATH Keywords: group of isometries
zbMATH Keywords: maximal compact subgroup
zbMATH Keywords: Fourier transform
MaRDI profile type: Publication
full work available at URL: pjm.1988.133.197
OpenAlex ID: W2095114771
DOI: 10.2140/PJM.1988.133.197
description: scientific article; zbMATH DE number 4021849