Bounded point derivations on certain function algebras

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

2 Scopus citations

Abstract

Let X be a compact nowhere dense subset of the complex plane ℂ, let C(X) be the linear space of all continuous functions on X endowed with the uniform norm, and let dA denote two-dimensional Lebesgue (or area) measure in ℂ. Denote by R(X) the closure in C(X) of the set of all rational functions having no poles on X. It is well known that if X is sufficiently massive, then the functions in R(X) can inherit many of the properties usually associated with the analytic functions, such as unlimited degrees of differentiability and even the uniqueness property itself. Here we shall examine the extent to which some of those properties are inherited by the larger algebra H(X), which by definition is the weak-* closure of R(X) in L(X) = L(X, dA).

Original languageEnglish
Title of host publicationOperator Theory
Subtitle of host publicationAdvances and Applications
Pages173-190
Number of pages18
DOIs
StatePublished - 2018

Publication series

NameOperator Theory: Advances and Applications
Volume261
ISSN (Print)0255-0156
ISSN (Electronic)2296-4878

Keywords

  • Analytic capacity
  • Monogeneity
  • Peak point
  • Point derivation
  • Swiss cheese
  • Wang’s theorem

ASJC Scopus subject areas

  • Analysis

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