On the direct cauchy theorem in widom domains: Positive and negative examples

Peter Yuditskii

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

We discuss several questions which remained open in our joint work with M. Sodin Almost periodic Jacobi matrices with homogeneous spectrum, in nite-dimensional Jacobi inversion, and Hardy spaces of character-automorphic functions. In particular, we show that there exists a nonhomogeneous set E such that the Direct Cauchy Theorem (DCT) holds in the Widom domain C\E. On the other hand we demonstrate that the weak homogeneity condition on E (introduced recently by Poltoratski and Remling) does not ensure that DCT holds in the corresponding Widom domain.

Original languageEnglish
Pages (from-to)395-414
Number of pages20
JournalComputational Methods and Function Theory
Volume11
Issue number2
DOIs
StatePublished - Jan 2012
Externally publishedYes

Bibliographical note

Funding Information:
Supported by the Austrian Science Fund FWF, project no: P22025-N18

Keywords

  • Direct Cauchy Theorem
  • Entire functions
  • Hardy spaces on Riemann surfaces
  • Homogeneous set
  • Martin function
  • Reflectionless Jacobi matrices
  • Widom domain

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