The Mellin-Whittaker integral transform
type: Item
instance of: scholarly article
title: The Mellin-Whittaker integral transform
zbMATH Open document ID: 0618.44001
DOI: 10.1007/BF01157027
author: V.-B. K. Rogov
published in: Mathematical Notes
publication date: 1986-01-01T00:00:00Z
review text: The author gives an inversion formula for the integral transform \(\iint K(\xi,\eta,\alpha,\beta,\lambda)f(\xi,\eta,\lambda)d\xi d\eta =F(\alpha,\beta,\lambda)\) with the kernel \[ K=\{(2\lambda)^{2i\alpha +1}B(i(\alpha +\beta)+1/2,i(\alpha -\beta)+1/2)/_{2\Gamma (2i\alpha +1)}\}\cdot \] \[ \eta^{2i}e^{\beta \pi sign \xi \eta -i\lambda \xi \eta}\Phi (i(\alpha +\beta)+1/2,2i\alpha +1,2i\lambda \xi \eta), \] where \(\Phi\) is the degenerate hypergeometric function. The mentioned integral transform sends the Laplace-Beltrami operator \(\partial^ 2/\partial \xi \partial \eta +i\lambda (\xi \partial /\partial \xi -\eta \partial /\partial \eta)\) appearing in the theory of symmetrical spaces into a multiplication by a function.
Mathematics Subject Classification ID: 44A15
zbMATH DE Number: 4002768
zbMATH Keywords: Mellin-Whittaker integral transform
zbMATH Keywords: inversion formula
zbMATH Keywords: degenerate hypergeometric function
zbMATH Keywords: Laplace-Beltrami operator
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4002768