On a Problem of Beurling

Brennan, J.

doi:10.1090/spmj/1527

On a Problem of Beurling
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by J. E. Brennan

St. Petersburg Math. J. 30 (2019), 1-13

DOI: https://doi.org/10.1090/spmj/1527

Published electronically: December 5, 2018

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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 $90$th 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.

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