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

DOI:
https://doi.org/10.1090/S0002-9947-1993-1038014-4

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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1993-1038014-4

Keywords:
Sieved polynomials,
polynomial mappings,
Julia sets,
generalized polynomial mappings,
-ultraspherical polynomials,
measures,
moment problem,
continued fractions

Article copyright:
© Copyright 1993
American Mathematical Society