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Author(s): Yakubovich, SB
Title: New index transforms of the Lebedev-Skalskaya type
Issue Date: 2016
Abstract: New index transforms, involving the real part of the modified Bessel function of the first kind as the kernel are considered. Mapping properties such as the boundedness and invertibility are investigated for these operators in the Lebesgue spaces. Inversion theorems are proved. As an interesting application, a solution of the initial value problem for the second-order partial differential equation, involving the Laplacian, is obtained. It is noted that the corresponding operators with the imaginary part of the modified Bessel function of the first kind lead to the familiar Kontorovich-Lebedev transform and its inverse.
Document Type: Artigo em Revista Científica Internacional
Rights: openAccess
Appears in Collections:FCUP - Artigo em Revista Científica Internacional

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