Toeplitz operators of finite interval type and the table method

M. C. Câmara, C. Diogo, I. M. Spitkovsky

Research output: Contribution to journalArticle

Abstract

We solve a Riemann-Hilbert problem with almost periodic coefficient G, associated to a Toeplitz operator TG in a class which is closely connected to finite interval convolution equations, based on a generalization of the so-called table method. The explicit determination of solutions to that problem allows one to establish necessary and sufficient conditions for the invertibility of the corresponding Toeplitz operator, and to determine an appropriate factorization of G, providing explicit formulas for the inverse of TG. Some unexpected properties of the Fourier spectrum of the solutions are revealed which are not apparent through other approaches to the same problem.

Original languageEnglish (US)
Pages (from-to)1148-1173
Number of pages26
JournalJournal of Mathematical Analysis and Applications
Volume432
Issue number2
DOIs
StatePublished - Dec 15 2015

Keywords

  • Almost periodic function
  • Factorization theory
  • Riemann-Hilbert problem
  • Toeplitz operator

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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