The continuous -Jacobi transform and its inverse when 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 -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

DOI:
https://doi.org/10.1090/S0002-9947-1988-0924774-5

Keywords:
Jacobi functions,
inverse transform,
Shannon sampling theorem

Article copyright:
© Copyright 1988
American Mathematical Society