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Uniform Approximation of Extremal Functions in Weighted Bergman Spaces

Uniform Approximation of Extremal Functions in Weighted Bergman Spaces We discuss approximation of extremal functions by polynomials in the weighted Bergman spaces $$A^p_\alpha $$ A α p where $$-1< \alpha < \min (0,p-2)$$ - 1 < α < min ( 0 , p - 2 ) . We obtain bounds on how close the approximation is to the true extremal function in the $$A^p_\alpha $$ A α p and uniform norms. We also prove several results on the relation between the Bergman modulus of continuity of a function and how quickly its best polynomial approximants converge to it. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

Uniform Approximation of Extremal Functions in Weighted Bergman Spaces

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References (18)

Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/s40315-017-0230-2
Publisher site
See Article on Publisher Site

Abstract

We discuss approximation of extremal functions by polynomials in the weighted Bergman spaces $$A^p_\alpha $$ A α p where $$-1< \alpha < \min (0,p-2)$$ - 1 < α < min ( 0 , p - 2 ) . We obtain bounds on how close the approximation is to the true extremal function in the $$A^p_\alpha $$ A α p and uniform norms. We also prove several results on the relation between the Bergman modulus of continuity of a function and how quickly its best polynomial approximants converge to it.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Jan 24, 2018

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