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2012 A New Kontorovich-Lebedev-Like Transformation
S. Yakubovich
Commun. Math. Anal. 13(1): 86-99 (2012).

Abstract

A different application of the familiar integral representation for the modified Bessel function drives to a new Kontorovich-Lebedev-like integral transformation of a general complex index. Mapping and operational properties, a convolution operator and inversion formula are established. Solvability conditions and explicit solutions of the corresponding class of convolution integral equations are exhibited. Finally, as a valuable application it is shown, that the introduced transformation is a key ingredient for solving difference equations of the order $n \in \mathbb{N}$ with constant coefficients in a class of analytic functions in the right half-plane ${\rm Re} z > n.$

Citation

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S. Yakubovich. "A New Kontorovich-Lebedev-Like Transformation." Commun. Math. Anal. 13 (1) 86 - 99, 2012.

Information

Published: 2012
First available in Project Euclid: 2 October 2012

zbMATH: 1262.44003
MathSciNet: MR2998349

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Rights: Copyright © 2012 Mathematical Research Publishers

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Vol.13 • No. 1 • 2012
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