An analogue of Hardy's theorem for very rapidly decreasing functions on semi-simple Lie groups
type: Item
instance of: scholarly article
title: An analogue of Hardy's theorem for very rapidly decreasing functions on semi-simple Lie groups
zbMATH Open document ID: 0882.43005
published in: Pacific Journal of Mathematics
publication date: 1998-02-01T00:00:00Z
review text: The main result is a generalization of a theorem of Hardy saying that a function on the real line and its Fourier transform cannot both be ``very rapidly decreasing'' to all noncompact semisimple Lie groups with finite center and one conjugacy class of Cartan subgroups. The result is also extended to \(\text{SL}(2,R)\) and to symmetric spaces of noncompact type. Such results can be viewed as uncertainty principles.
Mathematics Subject Classification ID: 43A30
Mathematics Subject Classification ID: 22E46
zbMATH DE Number: 1054235
zbMATH Keywords: Fourier transforms of rapidly decreasing functions on semisimple Lie groups
author: Alladi Sitaram
author: Maddala Sundari
reviewed by: Audrey A. Terras
Wikidata QID: Q115230700
MaRDI profile type: Publication
full work available at URL: pjm.1997.177.187
OpenAlex ID: W2164166717
DOI: 10.2140/PJM.1997.177.187
description: scientific article; zbMATH DE number 1054235