Sieved orthogonal polynomials and discrete measures with jumps dense in an interval
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- by Walter Van Assche and Alphonse P. Magnus
- Proc. Amer. Math. Soc. 106 (1989), 163-173
- DOI: https://doi.org/10.1090/S0002-9939-1989-0953001-4
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Abstract:
We investigate particular classes of sieved Jacobi polynomials for which the weight function vanishes at the zeros of a Chebyshev polynomial of the first kind. These polynomials are then used to give a proof, using only orthogonal polynomials on $[-1,1]$, that the discrete orthogonal polynomials introduced by Lubinsky have converging recurrence coefficients. We construct similar discrete measures with jumps dense in $[-1,1]$ and use sieved ultraspherical polynomials to show that their recurrence coefficients converge.References
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Bibliographic Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 106 (1989), 163-173
- MSC: Primary 42C05; Secondary 33A65
- DOI: https://doi.org/10.1090/S0002-9939-1989-0953001-4
- MathSciNet review: 953001