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 1 2006

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ASJC Scopus subject areas

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

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