International Journal of Mathematics and Mathematical Sciences
Volume 3 (1980), Issue 4, Pages 773-787
doi:10.1155/S0161171280000567
Expansions of distributions in terms of generalized heat polynomials and their Appell transforms
R.S. Pathak1
and Lokenath Debnath2
1Department of Mathematics, Banaras Hindu University, Varanasi, India
2Mathematical Institute, University of Oxford, Oxford, UK
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.