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

Ahmed I. Zayed

 Department of Mathematics, California Polytechnic State University, San Luis Obispo 93407, CA, USA
Received 19 August 1986; Revised 10 September 1986

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.