On a problem of Beurling

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This article is an extended version of a lecture presented to a conference at Brown University on 11 June 2017 in celebration of John Wermer's 90th birthday. Here, we discuss a complete solution to the weighted approximation problem for polynomials on an arbitrary bounded simply connected domain Ω in the complex plane. The problem had been studied extensively by Keldysh [13] prior to 1941 in the context of weighted L 2 -approximation, and more recently by Beurling [5], where the emphasis is on uniform approximation.

Original languageEnglish
Pages (from-to)1-13
Number of pages13
JournalSt. Petersburg Mathematical Journal
Issue number1
StatePublished - 2019

Bibliographical note

Publisher Copyright:
© 2018 American Mathematical Society.


  • Asymptotically holomorphic functions
  • Harmonic measure
  • Quasi-analyticity
  • Weighted polynomial approximation

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics


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