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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Complex equilibrium measure and Bernstein type theorems for compact sets in $\textbf {R}^ n$
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by Mirosław Baran PDF
Proc. Amer. Math. Soc. 123 (1995), 485-494 Request permission

Abstract:

The aim of this paper is to refine and develop further some results from a paper of Bedford and Taylor [Trans. Amer. Math. Soc. 294 (1986), 705-717]. The main result, a Bernstein type theorem, is an improvement of the classical Bernstein inequality \[ |p’(x)| \leq (\deg p){(1 - {x^2})^{ - 1/2}}{(\left \| p \right \|_{[ - 1,1]}^2 - {p^2}(x))^{1/2}},\] from the interval $[ - 1,1]$ to the multivariate case.
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 123 (1995), 485-494
  • MSC: Primary 31C10; Secondary 32F05, 32F07
  • DOI: https://doi.org/10.1090/S0002-9939-1995-1219719-6
  • MathSciNet review: 1219719