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2016 Lebedev's Type Index Transforms with the Modified Bessel Functions
Semyon Yakubovich
Commun. Math. Anal. 19(2): 68-81 (2016).


New index transforms of the Lebedev type are investigated. It involves the real part of the product of the modified Bessel functions as the kernel. Boundedness properties are examined for these operators in the Lebesgue weighted spaces. Inversion theorems are proved. Important particular cases are exhibited. The results are applied to solve an initial value problem for the fourth order PDE, involving the Laplacian. Finally, it is shown that the same PDE has another fundamental solution, which is associated with the generalized Lebedev index transform, involving the square of the modulus of Macdonald's function, recently considered by the author.


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Semyon Yakubovich. "Lebedev's Type Index Transforms with the Modified Bessel Functions." Commun. Math. Anal. 19 (2) 68 - 81, 2016.


Published: 2016
First available in Project Euclid: 14 September 2016

zbMATH: 1348.44006
MathSciNet: MR3512605

Primary: 33C10 , 44A05 , 44A15

Keywords: Fourier transform , Index Transform , Initial value problem , Lebedev transform , Mellin transform , modified Bessel functions

Rights: Copyright © 2016 Mathematical Research Publishers


Vol.19 • No. 2 • 2016
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