On orthogonal polynomials with respect to varying measures on the unit circle
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- by K. Pan PDF
- Trans. Amer. Math. Soc. 346 (1994), 331-340 Request permission
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 $d\mu /|{w_n}(z){|^2},\;z = {e^{i\theta }}$, where $\{ {w_n}(z)\}$ is a sequence of polynomials, $\deg {w_n} = n$, whose zeros ${w_{n,1}}, \ldots ,{w_{n,n}}$ lie in $|z| < 1$ The asymptotic behavior of the ratio of the two systems on and outside the unit circle is obtained.References
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Additional Information
- © Copyright 1994 American Mathematical Society
- 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