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

F. Peherstorfer, A. Volberg, P. Yuditskii

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)264-272
Number of pages9
JournalFunctional Analysis and its Applications
Volume40
Issue number4
DOIs
StatePublished - 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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