New inversion, convolution and Titchmarsh's theorems for the half-Hartley transform
Classical Analysis and ODEs
2014-03-11 v2
Abstract
The generalized Parseval equality for the Mellin transform is employed to prove the inversion theorem in L_2 with the respective inverse operator related to the Hartley transform on the nonnegative half-axis (the half-Hartley transform). Moreover, involving the convolution method, which is based on the double Mellin-Barnes integrals, the corresponding convolution and Titchmarsh's theorems for the half-Hartley transform are established. As an application, we consider solvability conditions for a homogeneous integral equation of the second kind involving the Hartley kernel.
Cite
@article{arxiv.1401.3143,
title = {New inversion, convolution and Titchmarsh's theorems for the half-Hartley transform},
author = {Semyon Yakubovich},
journal= {arXiv preprint arXiv:1401.3143},
year = {2014}
}