Harmonic analysis of spherical functions on \(SU(1,1)\)
type: Item
instance of: scholarly article
title: Harmonic analysis of spherical functions on \(SU(1,1)\)
zbMATH Open document ID: 0763.43006
author: Y. Weit
author: Yoav Benyamini
publication date: 1993-02-08T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/74969
review text: Denote by \(L^ 1(K\backslash G/K)\) the algebra of spherical integrable functions on \(SU(1,1)\), with convolution as multiplication. This is a commutative semi-simple algebra, and we use its Gelfand transform to study the ideals in \(L^ 1(K\backslash G/K)\). In particular, we are interested in conditions on an ideal that ensure that it is all of \(L^ 1(K\backslash G/K)\), or that it is \(L_ 0^ 1(K\backslash G/K)\). Spherical functions on \(SU(1,1)\) are naturally represented as radial functions on the unit disk \(D\) in the complex plane. Using this representation, these results are applied to characterize harmonic and holomorphic functions on \(D\).
Mathematics Subject Classification ID: 43A90
Mathematics Subject Classification ID: 43A85
Mathematics Subject Classification ID: 43A20
zbMATH DE Number: 118279
zbMATH Keywords: spherical functions on \(SU(1,1)\)
zbMATH Keywords: algebra of spherical integrable functions
zbMATH Keywords: convolution
zbMATH Keywords: semi-simple algebra
zbMATH Keywords: Gelfand transform
zbMATH Keywords: ideals
zbMATH Keywords: radial functions
zbMATH Keywords: holomorphic functions
MaRDI profile type: Publication
OpenAlex ID: W2323805681
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DOI: 10.5802/AIF.1305
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 118279