Bernstein-Walsh theory associated to convex bodies and applications to multivariate approximation theory

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.


Publication Date:
Jan 19 2017
Date Submitted:
Mar 01 2019
Pagination:
361-388
Citation:
Computational Methods in Function Theory, 18, 2
Note:
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 Record created 2019-03-01, last modified 2019-04-03


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