New index transforms of the Lebedev- Skalskaya type
Classical Analysis and ODEs
2015-09-11 v2
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.
Keywords
Cite
@article{arxiv.1509.02764,
title = {New index transforms of the Lebedev- Skalskaya type},
author = {Semyon Yakubovich},
journal= {arXiv preprint arXiv:1509.02764},
year = {2015}
}