Multy-Dimentional Integral Transform with the Confluent Hypergeometric Kummer Function in the Kernel and Integral Equation of the First Kind

Abstract

Multy-dimentional integral transform involving Kummer function in the kernel is studied on the space of summable functions on a finite domain [a?, b?]*...*[ an b]n? R ?. Mapping properties such as the boundedness are given, and the inversion formula is established. Integral equation of the first kind with the Kummer function in the kernel is also considered. The solution of the investigating equation is established, and conditions for it solvability in the space of summable functions are given.