The growth of polynomials outside of a compact set—The Bernstein–Walsh inequality revisited

In this paper, we present a new and simple proof of the classical Bernstein–Walsh inequality. Based on this proof, we give some improvements for this inequality in the case that the corresponding compact set is real.

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Bibliographic Details
Published in:Journal of approximation theory 2017-11, Vol.223, p.9-18
Main Author: Schiefermayr, Klaus
Format: Article
Language:English
Subjects:
Bernstein–Walsh inequality
Green function
Inverse polynomial image
Logarithmic capacity
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Description
Summary:In this paper, we present a new and simple proof of the classical Bernstein–Walsh inequality. Based on this proof, we give some improvements for this inequality in the case that the corresponding compact set is real.
ISSN:0021-9045
1096-0430
DOI:10.1016/j.jat.2017.07.007