New index transforms with the product of Bessel functions

2015/01/19 by Semyon Yakubovich, Yakubovich, Semyon
Mathematics · #33C10 #44A05 #44A15 #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1501.04609

openalex publication_date 2015/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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