On the Weber integral equation and solution to the Weber-Titchmarsh problem
Classical Analysis and ODEs
2016-12-19 v1
Abstract
We derive sufficient conditions for the existence of the Weber formal solution of the corresponding integral equation, related to the familiar Weber-Orr integral transforms. This gives a solution to the old Weber-Titchmarsh problem (posed in Proc. Lond. Math. Soc. 22(2) (1924), pp.15, 16.) Our method involves properties of the inverse Mellin transform of integrable functions. The Mellin-Parseval equality and some integrals with the associated Legendre functions are used.
Cite
@article{arxiv.1612.05455,
title = {On the Weber integral equation and solution to the Weber-Titchmarsh problem},
author = {Semyon Yakubovich},
journal= {arXiv preprint arXiv:1612.05455},
year = {2016}
}