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International Journal of Mathematics and Mathematical Sciences
Volume 10, Issue 4, Pages 671-692
http://dx.doi.org/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 Hindawi Publishing Corporation. 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.