Rapid Polynomial Approximation on Stein Manifolds
| Autor: | Snaebjarnarson, Audunn Skuta |
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| Rok vydání: | 2016 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this paper we generalize to a certain class of Stein manifolds the Bernstein-Walsh-Siciak theorem which describes the equivalence between possible holomorphic continuation of a function $f$ defined on a compact set $K$ in $\mathbb{C}^N$ to the rapidity of the best uniform approximation of $f$ on $K$ by polynomials. We also generalize Winiarski's theorem which relates the growth rate of an entire function $f$ on $\mathbb{C}^N$ to its best uniform approximation by polynomials on a compact set. |
| Databáze: | arXiv |
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