International Journal of Mathematics and Mathematical Sciences
Volume 10 (1987), Issue 4, Pages 671-692
doi:10.1155/S0161171287000796
A generalized inversion formula for the continuous Jacobi transform
Department of Mathematics, California Polytechnic State University, San Luis Obispo 93407, CA, USA
Received 19 August 1986; Revised 10 September 1986
Copyright © 1987 Ahmed I. Zayed. 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.
Abstract
In this paper we extend the definition of the continuous Jacobi transform to a class of generalized functions and obtain a generalized inversion formula for it. As a by-product of our technique we obtain a necessary and sufficient condition for an analytic function F(λ) in Reλ>0 to be the continuous Jacobi transform of a generalized function.