Mehler integral transform associated with Jacobi functions with respect to the dual variable
type: Item
instance of: scholarly article
title: Mehler integral transform associated with Jacobi functions with respect to the dual variable
zbMATH Open document ID: 0889.43001
author: Khalifa Trimèche
author: Néjib Ben Salem
published in: Journal of Mathematical Analysis and Applications
publication date: 1998-05-25T00:00:00Z
review text: The paper deals with a Mehler representation for the Jacobi functions \(\varphi_\lambda^{(\alpha,\beta)}(t)\) with respect to the dual variable \(\lambda\). This representation is used to define a pair of dual transforms of Mehler type: \(\chi_{\alpha,\beta}\) and its transposed \(^t\chi_{\alpha,\beta}\). Two second order difference operators \(P_{\alpha,\beta}\) and \(Q\) are studied, such that the Jacobi function \(\varphi_\lambda^{(\alpha,\beta)}(t)\) is an eigenfunction of \(P_{\alpha,\beta}\) with respect to the dual variable, and \(\chi_{\alpha,\beta}\) and its transposed \(^t\chi_{\alpha,\beta}\) are permutation operators between \(P_{\alpha,\beta}\) and \(Q\). The authors study some spaces of functions on which both transforms are isomorphisms and they find inversion formulae for these transforms.
Mathematics Subject Classification ID: 43A32
Mathematics Subject Classification ID: 44A15
Mathematics Subject Classification ID: 33C45
zbMATH DE Number: 1123613
zbMATH Keywords: Jacobi functions
zbMATH Keywords: Mehler representation
zbMATH Keywords: Fourier-Jacobi integral transform
zbMATH Keywords: Mehler integral transform
MaRDI profile type: Publication
full work available at URL: jmaa.1997.5623
OpenAlex ID: W1972728513
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DOI: 10.1006/JMAA.1997.5623
description: scientific article; zbMATH DE number 1123613