Sieved orthogonal polynomials and discrete measures with jumps dense in an interval

Authors:
Walter Van Assche and Alphonse P. Magnus

Journal:
Proc. Amer. Math. Soc. **106** (1989), 163-173

MSC:
Primary 42C05; Secondary 33A65

MathSciNet review:
953001

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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 , that the discrete orthogonal polynomials introduced by Lubinsky have converging recurrence coefficients. We construct similar discrete measures with jumps dense in and use sieved ultraspherical polynomials to show that their recurrence coefficients converge.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1989-0953001-4

Keywords:
Sieved orthogonal polynomials,
Chebyshev polynomials,
Nevai's class

Article copyright:
© Copyright 1989
American Mathematical Society