Title

Generalized Jacobi Transform

Keywords

generalized functions; inverse Jacobi transform; Jacobi transform; sampling theorems

Abstract

Recently, Koornwinder and Walter derived an inversion formula for the finite continuous Jacobi transform for all α,β > -1. This inversion formula generalizes the one obtained earlier by Walter and Zayed for α,β > -1 and α + β is a non-negative integer. In this paper we extend the finite continuous Jacobi transform and its inversion formula as obtained by Koornwinder and Walter to generalized functions. In particular, a fundamental space will be constructed and the generalized transform will be defined on the dual space. Several properties of the generalized transform will be studied along with a generalized inversion formula. Some examples of the finite continuous Jacobi transform and its inversion formula will also be given. © 1993, Taylor & Francis Group, LLC. All rights reserved.

Publication Date

2-1-1993

Publication Title

Applicable Analysis

Volume

48

Issue

1-4

Number of Pages

63-79

Document Type

Article

Identifier

scopus

Personal Identifier

scopus

DOI Link

https://doi.org/10.1080/00036819308840150

Socpus ID

84948896605 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84948896605

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