Schwartz space for the hypergeometric Fourier transform. (With an appendix by Mustapha Tinfou)
type: Item
instance of: scholarly article
title: Schwartz space for the hypergeometric Fourier transform. (With an appendix by Mustapha Tinfou)
zbMATH Open document ID: 0934.43005
author: Patrick Delorme
published in: Journal of Functional Analysis
publication date: 2000-04-25T00:00:00Z
review text: The author determines the hypergeometric Fourier transform of the related Schwartz space of functions invariant under the Weyl group \((W\)-invariant functions) on a Euclidean vector space. The result is quite similar to that of Harish-Chandra. It is shown that the simple difference operators play the role of some elements of the unipotent radical of a parabolic subalgebra. This requires a theory of constant term for \(W\)-invariant functions satisfying the hypergeometric system. It is emphasized that the parameter of cuspidal hypergeometric functions can be singular and in such cases new difficulties appear. Finally, it is suggested that the techniques used for real reductive symmetric spaces can be applied to study truncation and its consequences.
Mathematics Subject Classification ID: 43A85
zbMATH DE Number: 1374986
zbMATH Keywords: hypergeometric Fourier transform
zbMATH Keywords: difference operators
zbMATH Keywords: unipotent radical
zbMATH Keywords: hypergeometric system
zbMATH Keywords: cuspidal hypergeometric functions
reviewed by: Gheorghe Zet
MaRDI profile type: Publication
full work available at URL: jfan.1999.3449
OpenAlex ID: W1987399019
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DOI: 10.1006/JFAN.1999.3449
description: scientific article; zbMATH DE number 1374986