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Norm asymptotics of orthogonal polynomials for general measures

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Abstract

Letμ be a fixed positive unit Borel measure with infinite support in the unit disk. Acarrier of μ is any Borel subsetB of the support for whichμ(B)=1, and another such measurev iscarrier-related to μ when it has the same carriers asμ. Letp n (z, v) be the monic orthogonal polynomial of degreen forv. We describe the possible asymptotics for the sequences {(∫|p n (z,v)|2 dv)1/2n} n≥1 which are associated to the set of measures carrier-related to μ.

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Authors and Affiliations

  1. Department of Mathematics, University of Michigan-Flint, 48502-2186, Flint, Michigan, USA

    M. F. Wyneken

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  1. M. F. Wyneken
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Communicated by Paul Nevai.

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Wyneken, M.F. Norm asymptotics of orthogonal polynomials for general measures. Constr. Approx 4, 123–131 (1988). https://doi.org/10.1007/BF02075453

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  • DOI: https://doi.org/10.1007/BF02075453

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