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New index transforms with the product of Bessel functions

Authors
  • Yakubovich, Semyon
Type
Preprint
Publication Date
Sep 05, 2015
Submission Date
Jan 19, 2015
Identifiers
arXiv ID: 1501.04609
Source
arXiv
License
Yellow
External links

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.

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