The continuous $(\alpha , \beta )$-Jacobi transform and its inverse when $\alpha +\beta +1$ is a positive integer
Authors:
G. G. Walter and A. I. Zayed
Journal:
Trans. Amer. Math. Soc. 305 (1988), 653-664
MSC:
Primary 44A15; Secondary 33A65
DOI:
https://doi.org/10.1090/S0002-9947-1988-0924774-5
MathSciNet review:
924774
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Abstract: The continuous $(\alpha , \beta )$-Jacobi transform is introduced as an extension of the discrete Jacobi transform by replacing the polynomial kernel by a continuous one. An inverse transform is found for both the standard and a modified normalization and applied to a version of the sampling theorem. An orthogonal system forming a basis for the range is shown to have some unusual properties, and is used to obtain the inverse.
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Additional Information
Keywords:
Jacobi functions,
inverse transform,
Shannon sampling theorem
Article copyright:
© Copyright 1988
American Mathematical Society