Sieved orthogonal polynomials. VII. Generalized polynomial mappings

Charris, Jairo A.; Ismail, Mourad E. H.

doi:10.1090/S0002-9947-1993-1038014-4

Sieved orthogonal polynomials. VII. Generalized polynomial mappings
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by Jairo A. Charris and Mourad E. H. Ismail

Trans. Amer. Math. Soc. 340 (1993), 71-93

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

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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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