A finite and an infinite Whittaker integral transform
type: Item
instance of: scholarly article
title: A finite and an infinite Whittaker integral transform
zbMATH Open document ID: 1055.44004
DOI: 10.1016/S0898-1221(03)90241-0
publication date: 2004-08-20T00:00:00Z
review text: Recently, the reviewer, \textit{Y. K. Tuan} and \textit{S. B. Yakubovich} [Q. J. Math. 51, No. 3, 371--383 (1998; Zbl 0972.44003)] investigated several Plancherel-type theorems for the Cherry transform (that is, an index transformation with the parabolic cylinder function or the Weber-Hermite function in the kernel) by relating it to a singular Sturm-Liouville problem on the whole line. The authors of the paper under review devote their attention to the construction and investigation of several finite and infinite Whittaker transforms arising from another Sturm-Liouville problem on a half line. Another closely-related work, dealing with an index transformation with the Whittaker \(W_{\kappa,\mu}\)-function in the kernel, was presented earlier by the reviewer, \textit{Yu. V. Vasil'ev} and \textit{S. B. Yakubovich} [Q. J. Math., Oxf. II. Ser. 49, No. 195, 375--394 (1998; Zbl 0912.44004)].
Mathematics Subject Classification ID: 44A15
Mathematics Subject Classification ID: 33C15
Mathematics Subject Classification ID: 34B24
Mathematics Subject Classification ID: 34B40
Mathematics Subject Classification ID: 34A25
zbMATH DE Number: 2093591
zbMATH Keywords: Integral transform
zbMATH Keywords: Singular Sturm-Liouville problem
zbMATH Keywords: Whittaker function
zbMATH Keywords: Cherry transform
zbMATH Keywords: index transformation
author: Fadhel Al-Musallam
author: Vu Kim Tuan
reviewed by: H. M. Srivastava
MaRDI profile type: Publication
cites work: Q3259158
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cites work: A whittaker transform over a half-line
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cites work: Q4039929
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full work available at URL: s0898-1221(03)90241-0
OpenAlex ID: W2087269345
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 2093591