A class of index transforms generated by the Mellin and Laplace operators
Classical Analysis and ODEs
2012-09-11 v1
Abstract
Classical integral representation of the Mellin type kernel in terms of the Laplace integral gives an idea to construct a new class of non-convolution (index) transforms. Particular examples give the Kontorovich-Lebedev-like transformation and new transformations with hypergeometric functions as kernels. Mapping properties and inversion formulas are obtained. Finally we prove a new inversion theorem for the modified Kontorovich-Lebedev transform
Keywords
Cite
@article{arxiv.1209.1799,
title = {A class of index transforms generated by the Mellin and Laplace operators},
author = {Semyon Yakubovich},
journal= {arXiv preprint arXiv:1209.1799},
year = {2012}
}