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Rapid polynomial approximation on Stein manifolds

Volume 122 / 2019

Auðunn Skúta Snæbjarnarson Annales Polonici Mathematici 122 (2019), 81-100 MSC: Primary 32E30; Secondary 32A22, 32Q28, 32D15. DOI: 10.4064/ap180711-13-11 Published online: 8 March 2019


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 $\mathbb {C}^N$ and 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.


  • Auðunn Skúta SnæbjarnarsonDepartment of Mathematics
    School of Engineering and Natural Sciences
    University of Iceland
    Dunhagi 5
    107 Reykjavík, Iceland

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