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Bernstein–Walsh Theory Associated to Convex Bodies and Applications to Multivariate Approximation Theory

Bernstein–Walsh Theory Associated to Convex Bodies and Applications to Multivariate Approximation... We prove a version of the Bernstein–Walsh theorem on uniform polynomial approximation of holomorphic functions on compact sets in several complex variables. Here we consider subclasses of the full polynomial space associated to a convex body P. As a consequence, we validate and clarify some observations of Trefethen in multivariate approximation theory. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

Bernstein–Walsh Theory Associated to Convex Bodies and Applications to Multivariate Approximation Theory

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Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer-Verlag GmbH Germany
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/s40315-017-0220-4
Publisher site
See Article on Publisher Site

Abstract

We prove a version of the Bernstein–Walsh theorem on uniform polynomial approximation of holomorphic functions on compact sets in several complex variables. Here we consider subclasses of the full polynomial space associated to a convex body P. As a consequence, we validate and clarify some observations of Trefethen in multivariate approximation theory.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Oct 24, 2017

References