Density of certain polynomial modules

A. D. Baranov, J. J. Carmona, K. Yu Fedorovskiy

Research output: Contribution to journalArticleResearchpeer-review

4 Citations (Scopus)

Abstract

© 2015 Elsevier Inc.. In this paper the problem of density in the space C(X), for a compact set X⊂C, of polynomial modules of the type p+zdq:p,q∈C[z] for integer d>1, as well as several related problems are studied. We obtain approximability criteria for Carathéodory compact sets using the concept of a d-Nevanlinna domain, which is a new special analytic characteristic of planar simply connected domains. In connection with this concept we study the problem of taking roots in the model spaces, that is, in the subspaces of the Hardy space H2 which are invariant under the backward shift operator.
Original languageEnglish
Pages (from-to)1-16
JournalJournal of Approximation Theory
Volume206
DOIs
Publication statusPublished - 1 Jun 2016

Keywords

  • Carathéodory sets
  • D-Nevanlinna domains
  • Model spaces K Θ
  • Polyanalytic polynomials
  • Rational modules
  • Uniform approximation

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