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
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.