New index transforms with the product of Bessel functions

DOI10.1080/10652469.2015.1070150zbMATH Open1336.44003arXiv1501.04609OpenAlexW2158217824MaRDI QIDQ3448971

S. Yakubovich

Publication date: 3 November 2015

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Abstract: New index transforms are investigated, which contain as the kernel products of the Bessel and modified Bessel functions. Mapping properties and invertibility in Lebesgue spaces are studied for these operators. Relationships with the Kontorovich-Lebedev and Fourier cosine transforms are established. Inversion theorems are proved. As an application, a solution of the initial value problem for the fourth order partial differential equation, involving the Laplacian is presented.

Full work available at URL: https://arxiv.org/abs/1501.04609

zbMATH Keywords

Fourier transformMellin transformmodified Bessel functionsinversion theoremBessel functionsKontorovich-Lebedev transformindex transforms

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10)

Cites Work

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Related Items (4)

A double index transform with a product of Macdonald's functions revisited ⋮ Lebedev type index transforms with the squares of the associated {L}egendre functions ⋮ Discrete index transformations with Bessel and Lommel functions ⋮ Discrete index transformations with squares of Bessel functions

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