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Статья «ON A PROBLEM OF BEURLING, "Алгебра и анализ"»

Авторы:
  • BRENNAN J. E.1
стр. 1-19
Платно
1 University of Kentucky
  • SDI: 007.001.0234-0852.2018.030.001.1
Ключевые слова:
  • weighted polynomial approximation
  • quasi-analyticity
  • asymptotically holomorphic functions
  • harmonic measure
Аннотация:
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 fl in the complex plane. The problem had been studied extensively by Keldysh [13] prior to 1941 in the context of weighted /©approximation, and more recently by Beurling [5], where the emphasis is on uniform approximation.

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