One-dimensional and multi-dimensional integral transforms of Buschman-Erdélyi type with Legendre functions in kernels

Abstract

This paper consists of two parts. In the first part we give a brief survey of results on Buschman-Erdélyi operators, which are transmutations for the Bessel singular operator. Main properties and applications of Buschman-Erdélyi operators are outlined. In the second part of the paper we consider multi-dimensional integral transforms of Buschman-Erdélyi type with Legendre functions in kernels. Complete proofs are given in this part, main tools are based onMellin transformproperties and usage of Fox H-functions