Index transforms with the square of Bessel functions
Classical Analysis and ODEs
2015-10-20 v2
Abstract
New index transforms, involving the square of Bessel functions 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 to the initial value problem for the third order partial differential equation, involving the Laplacian, is obtained.
Cite
@article{arxiv.1509.08723,
title = {Index transforms with the square of Bessel functions},
author = {Semyon Yakubovich},
journal= {arXiv preprint arXiv:1509.08723},
year = {2015}
}
Comments
arXiv admin note: text overlap with arXiv:1509.02764