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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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 $ [-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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0953001-4
PII: S 0002-9939(1989)0953001-4
Keywords: Sieved orthogonal polynomials, Chebyshev polynomials, Nevai's class $ M(a,b)$
Article copyright: © Copyright 1989 American Mathematical Society