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On orthogonal polynomials with respect to varying measures on the unit circle


Author: K. Pan
Journal: Trans. Amer. Math. Soc. 346 (1994), 331-340
MSC: Primary 42C05
DOI: https://doi.org/10.1090/S0002-9947-1994-1273539-9
MathSciNet review: 1273539
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Abstract: Let $ \{ {\phi _n}(d\mu )\} $ be a system of orthonormal polynomials on the unit circle with respect to $ d\mu $ and $ \{ {\psi _{n,m}}(d\mu )\} $ be a system of orthonormal polynomials on the unit circle with respect to the varying measures $ d\mu /\vert{w_n}(z){\vert^2},\;z = {e^{i\theta }}$, where $ \{ {w_n}(z)\} $ is a sequence of polynomials, $ \deg {w_n} = n$, whose zeros $ {w_{n,1}}, \ldots ,{w_{n,n}}$ lie in $ \vert z\vert < 1$ The asymptotic behavior of the ratio of the two systems on and outside the unit circle is obtained.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1994-1273539-9
Keywords: Orthogonal polynomials, asymptotic properties
Article copyright: © Copyright 1994 American Mathematical Society

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