A finite and an infinite Whittaker integral transform
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)].
scientific article; zbMATH DE number 2093591
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