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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- © Copyright 1988 American Mathematical Society
- 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