4 research outputs found

    Generalized Jacobi Transform

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    Recently, Koornwinder and Walter derived an inversion formula for the finite continuous Jacobi transform for all α,β \u3e -1. This inversion formula generalizes the one obtained earlier by Walter and Zayed for α,β \u3e -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
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