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ЖУРНАЛЫ // Алгебра и анализ // Архив

Алгебра и анализ, 2018, том 30, выпуск 1, страницы 1–19 (Mi aa1569)

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On a problem of Beurling

J. E. Brennan

Department of Mathematics, University of Kentucky, Lexington, KY, 40506, USA

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 $\Omega$ 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.

Ключевые слова: weighted polynomial approximation, quasi-analyticity, asymptotically holomorphic functions, harmonic measure.

MSC: 30E10

Поступила в редакцию: 25.09.2017

Язык публикации: английский


 Англоязычная версия: St. Petersburg Mathematical Journal, 2019, 30:1, 1–13

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