A new Kontorovich-Lebedev-like transformation

TL;DR

This paper introduces a novel Kontorovich-Lebedev-like integral transformation based on a new application of the modified Bessel function's integral representation, including properties, convolution, inversion, and solutions.

Contribution

It presents a new integral transformation with its properties, convolution operator, inversion formula, and solvability conditions, expanding the mathematical tools for complex analysis.

Findings

Established mapping and operational properties.

Derived an explicit inversion formula.

Solved a class of convolution integral equations.

Abstract

A different application of the familiar integral representation for the modifed Bessel function drives to a new Kontorovich-Lebedev-like integral transformation of a general complex index. Mapping and operational properties, a convolution operator and inversion formula are established. Solvability conditions and explicit solutions of the corresponding class of convolution integral equations are exhibited.