On Gauss-Weierstrass semigroups and inversion of potentials associated with the Bessel differential operator

Abstract

In this paper, we define the generalized Gauss-Weierstrass semigroups with Weierstrass kernel, and give some of their properties. Using them, we study the inversion formulas for the generalized Riesz and Bessel potentials, generated by the generalized shift operators and associated with the Laplace Bessel differential operator.