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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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The continuous $(\alpha , \beta )$-Jacobi transform and its inverse when $\alpha +\beta +1$ is a positive integer
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by G. G. Walter and A. I. Zayed PDF
Trans. Amer. Math. Soc. 305 (1988), 653-664 Request permission


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
  • © Copyright 1988 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 305 (1988), 653-664
  • MSC: Primary 44A15; Secondary 33A65
  • DOI:
  • MathSciNet review: 924774