On the Kontorovich-Lebedev transform
type: Item
instance of: scholarly article
zbMATH Open document ID: 1259.44003
author: Dorian Goldfeld
author: Eric Stade
author: Alex Kontorovich
publication date: 2012-09-07T00:00:00Z
Mathematics Subject Classification ID: 44A15
zbMATH DE Number: 6079039
zbMATH Keywords: Macdonald-Bessel function
zbMATH Keywords: integral transform
zbMATH Keywords: Kontorovich-Lebedev transform
zbMATH Keywords: inversion formula
MaRDI profile type: Publication
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title: On the Kontorovich-Lebedev transform
published in: Commentarii Mathematici Universitatis Sancti Pauli
review text: The authors consider the Kontorovich-Lebedev transform in the form NEWLINE\[NEWLINEg(t)= \int^\infty_0 f(x)\,K_{it}(x){dx\over x},NEWLINE\]NEWLINE where \(K_{it}\) is the Macdonald-Bessel function, and give a proof of the inversion formula. The proof is based on the evaluation of the integral NEWLINE\[NEWLINE\int^\infty_{-\infty} K_{it}(x)\,K_{it}(y)\, K_{it}(z){dt\over \Gamma(it)\Gamma(-it)},NEWLINE\]NEWLINE which is interesting by itself.
reviewed by: Khristo N. Boyadzhiev
description: scientific article; zbMATH DE number 6079039