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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

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
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

DOI: http://dx.doi.org/10.1090/S0002-9947-1988-0924774-5
PII: S 0002-9947(1988)0924774-5
Keywords: Jacobi functions, inverse transform, Shannon sampling theorem
Article copyright: © Copyright 1988 American Mathematical Society