Generalized convolution for the discrete Jacobi transformation (Q1872899)

The authors consider the finite Jacobi transformation and the discrete Jacobi transform and analyse some topological questions about the spaces on which the finite Jacobi transform acts and develop a systematical and complete investigation of the discrete transform. Firstly, this transform is studied in a space of sequences of rapid descend and its dual, and the main properties of these spaces and those ones of the corresponding multiplier spaces are established. Next, they deal in detail with the discrete translation operator and the discrete convolution associated to the discrete Jacobi transformation. Finally, it is shown that the discrete Jacobi transformation generates an operational calculus that can be used to find the solution of some finite difference equations.