Expansions of distributions in terms of generalized heat polynominals and their Appell transforms

Abstract

This paper is concerned with expansions of distributions in terms of the generalized heat polynomials and of their Appell transforms. Two different techniques are used to prove theorems concerning expansions of distributions. A theorem which provides an orthogonal series expansion of generalized functions is also established. It is shown that this theorem gives an inversion formula for a certain generalized integral transformation.

Keywords

• expansion of distributions (or generalized functions)
• generalized heat polynomials and their Appell transforms
• orthogonal series expansion of generalized functions and generalized integral transformation.