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.
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Communicated by Doron Lubinsky.
N. Levenberg has been supported by Simons Foundation Grant no. 354549.
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Bos, L., Levenberg, N. Bernstein–Walsh Theory Associated to Convex Bodies and Applications to Multivariate Approximation Theory. Comput. Methods Funct. Theory 18, 361–388 (2018). https://doi.org/10.1007/s40315-017-0220-4
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DOI: https://doi.org/10.1007/s40315-017-0220-4