International Journal of Mathematics and Mathematical Sciences
Volume 3 (1980), Issue 4, Pages 773-787

Expansions of distributions in terms of generalized heat polynominals 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

Received 13 November 1978; Revised 15 July 1980

Copyright © 1980 R. S. Pathak and Lokenath Debnath. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.