On a problem of Beurling

J. E. Brennan

doi:10.1090/spmj/1527

On a problem of Beurling

J. E. Brennan

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Pages (from-to)	1-13
Number of pages	13
Journal	St. Petersburg Mathematical Journal
Volume	30
Issue number	1
DOIs	https://doi.org/10.1090/spmj/1527
State	Published - 2019

Bibliographical note

Publisher Copyright:
© 2018 American Mathematical Society.

Keywords

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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AB - 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.

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On a problem of Beurling

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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