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Transactions of the American Mathematical Society

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

 

 

Sieved orthogonal polynomials. VII. Generalized polynomial mappings


Authors: Jairo A. Charris and Mourad E. H. Ismail
Journal: Trans. Amer. Math. Soc. 340 (1993), 71-93
MSC: Primary 33C45
MathSciNet review: 1038014
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Abstract: Systems of symmetric orthogonal polynomials whose recurrence relations are given by compatible blocks of second-order difference equations are studied in detail. Applications are given to the theory of the recently discovered sieved orthogonal polynomials. The connection with polynomial mappings is examined. An example of a family of orthogonal polynomials having discrete masses in the interior of the spectrum is included.


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DOI: https://doi.org/10.1090/S0002-9947-1993-1038014-4
Keywords: Sieved polynomials, polynomial mappings, Julia sets, generalized polynomial mappings, $ q$-ultraspherical polynomials, measures, moment problem, continued fractions
Article copyright: © Copyright 1993 American Mathematical Society