Generalized Jacobi transform
Ahmed I. Zayed, Elias Y. Deeba · Applicable Analysis · 1993
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.