Asymptotics of orthogonal polynomials beyond the scope of Szego's theorem

F. Peherstorfer; A. Volberg; P. Yuditskii

doi:10.1007/s10688-006-0043-y

Asymptotics of orthogonal polynomials beyond the scope of Szego's theorem

F. Peherstorfer, A. Volberg, P. Yuditskii

Department of Mathematics

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

Abstract

First, we give a simple proof of a remarkable result due to Videnskii and Shirokov: let B be a Blaschke product with n zeros; then there exists an outer function φ, φ(0) = 1, such that ∥(Bφ)∥≤ Cn, where C is an absolute constant. Then we apply this result to a certain problem of finding the asymptotics of orthogonal polynomials.

Original language	English
Pages (from-to)	264-272
Number of pages	9
Journal	Functional Analysis and its Applications
Volume	40
Issue number	4
DOIs	https://doi.org/10.1007/s10688-006-0043-y
State	Published - Oct 2006

Bibliographical note

Funding Information:
∗The research of the first author was partially supported by the Austrian Science Fund FWF, project P16390-N04. The research of the second author was partially supported by NSF grant DMS-0200713. The research of the third author was partially supported by the Marie Curie Fund, contract MIF1-CT-2005-006966.

Keywords

Blaschke product
CMV matrix
Extremal problem
Orthogonal polynomial

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10.1007/s10688-006-0043-y

Cite this

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abstract = "First, we give a simple proof of a remarkable result due to Videnskii and Shirokov: let B be a Blaschke product with n zeros; then there exists an outer function φ, φ(0) = 1, such that ∥(Bφ)∥≤ Cn, where C is an absolute constant. Then we apply this result to a certain problem of finding the asymptotics of orthogonal polynomials.",

keywords = "Blaschke product, CMV matrix, Extremal problem, Orthogonal polynomial",

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note = "Funding Information: ∗The research of the first author was partially supported by the Austrian Science Fund FWF, project P16390-N04. The research of the second author was partially supported by NSF grant DMS-0200713. The research of the third author was partially supported by the Marie Curie Fund, contract MIF1-CT-2005-006966.",

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AU - Peherstorfer, F.

AU - Volberg, A.

AU - Yuditskii, P.

N1 - Funding Information: ∗The research of the first author was partially supported by the Austrian Science Fund FWF, project P16390-N04. The research of the second author was partially supported by NSF grant DMS-0200713. The research of the third author was partially supported by the Marie Curie Fund, contract MIF1-CT-2005-006966.

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N2 - First, we give a simple proof of a remarkable result due to Videnskii and Shirokov: let B be a Blaschke product with n zeros; then there exists an outer function φ, φ(0) = 1, such that ∥(Bφ)∥≤ Cn, where C is an absolute constant. Then we apply this result to a certain problem of finding the asymptotics of orthogonal polynomials.

AB - First, we give a simple proof of a remarkable result due to Videnskii and Shirokov: let B be a Blaschke product with n zeros; then there exists an outer function φ, φ(0) = 1, such that ∥(Bφ)∥≤ Cn, where C is an absolute constant. Then we apply this result to a certain problem of finding the asymptotics of orthogonal polynomials.

KW - Blaschke product

KW - CMV matrix

KW - Extremal problem

KW - Orthogonal polynomial

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JO - Functional Analysis and its Applications

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IS - 4

ER -

Asymptotics of orthogonal polynomials beyond the scope of Szego's theorem

Abstract

Bibliographical note

Keywords

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