Asymptotic behaviour of orthogonal polynomials on the unit circle with asymptotically periodic reflection coefficients II, Weak asymptotics

Franz Peherstorfer; Robert Steinbauer

doi:10.1006/jath.2000.3450

Asymptotic behaviour of orthogonal polynomials on the unit circle with asymptotically periodic reflection coefficients II, Weak asymptotics

Franz Peherstorfer
, Robert Steinbauer

Department of Dynamic Systems and Approximation Theory

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper we study orthogonal polynomials with asymptotically periodic reflection coefficients. It's known that the support of the orthogonality measure of such polynomials consists of several arcs. We are mainly interested in the asymptotic behaviour on the support and derive weak convergence results for the orthogonal polynomials and also for the Christoffel function.

Original language	English
Pages (from-to)	102-128
Number of pages	27
Journal	Journal of Approximation Theory
Volume	105
Issue number	1
DOIs	https://doi.org/10.1006/jath.2000.3450
Publication status	Published - Jul 2000

Fields of science

101002 Analysis
101027 Dynamical systems
103019 Mathematical physics
101031 Approximation theory

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10.1006/jath.2000.3450

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abstract = "In this paper we study orthogonal polynomials with asymptotically periodic reflection coefficients. It's known that the support of the orthogonality measure of such polynomials consists of several arcs. We are mainly interested in the asymptotic behaviour on the support and derive weak convergence results for the orthogonal polynomials and also for the Christoffel function.",

author = "Franz Peherstorfer and Robert Steinbauer",

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AU - Steinbauer, Robert

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N2 - In this paper we study orthogonal polynomials with asymptotically periodic reflection coefficients. It's known that the support of the orthogonality measure of such polynomials consists of several arcs. We are mainly interested in the asymptotic behaviour on the support and derive weak convergence results for the orthogonal polynomials and also for the Christoffel function.

AB - In this paper we study orthogonal polynomials with asymptotically periodic reflection coefficients. It's known that the support of the orthogonality measure of such polynomials consists of several arcs. We are mainly interested in the asymptotic behaviour on the support and derive weak convergence results for the orthogonal polynomials and also for the Christoffel function.

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DO - 10.1006/jath.2000.3450

M3 - Article

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JO - Journal of Approximation Theory

JF - Journal of Approximation Theory

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Asymptotic behaviour of orthogonal polynomials on the unit circle with asymptotically periodic reflection coefficients II, Weak asymptotics

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