A Riemann-Hilbert approach to some theorems on Toeplitz operators and orthogonal polynomials

Percy Deift, Jörgen Östensson

Research output: Contribution to journalArticle

Abstract

In this paper, the authors show how to use Riemann-Hilbert techniques to prove various results, some old, some new, in the theory of Toeplitz operators and orthogonal polynomials on the unit circle (OPUCs). There are four main results: the first concerns the approximation of the inverse of a Toeplitz operator by the inverses of its finite truncations. The second concerns a new proof of the 'hard' part of Baxter's theorem, and the third concerns the Born approximation for a scattering problem on the lattice Z +. The fourth and final result concerns a basic proposition of Golinskii-Ibragimov arising in their analysis of the Strong Szegö Limit Theorem.

Original languageEnglish (US)
Pages (from-to)144-171
Number of pages28
JournalJournal of Approximation Theory
Volume139
Issue number1-2
DOIs
StatePublished - Mar 2006

Fingerprint

Born approximation
Toeplitz Operator
Orthogonal Polynomials
Hilbert
Mathematical operators
Polynomials
Scattering
Theorem
Strong Limit Theorem
Born Approximation
Scattering Problems
Unit circle
Truncation
Proposition
Approximation

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Mathematics(all)
  • Numerical Analysis

Cite this

A Riemann-Hilbert approach to some theorems on Toeplitz operators and orthogonal polynomials. / Deift, Percy; Östensson, Jörgen.

In: Journal of Approximation Theory, Vol. 139, No. 1-2, 03.2006, p. 144-171.

Research output: Contribution to journalArticle

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