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Transactions of the American Mathematical Society

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Approximation of analytic functions on compact sets and Bernstein's inequality

Authors: M. S. Baouendi and C. Goulaouic
Journal: Trans. Amer. Math. Soc. 189 (1974), 251-261
MSC: Primary 41A10
MathSciNet review: 0352789
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Abstract: The characterization of analytic functions defined on a compact set K in $ {{\mathbf{R}}_N}$ by their polynomial approximation is possible if and only if K satisfies some ``Bernstein type inequality", estimating any polynomial P in some neighborhood of K using the supremum of P on K. Some criterions and examples are given. Approximation by more general sets of analytic functions is also discussed.

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Keywords: Approximation of real-analytic functions, polynomials, Bernstein inequality
Article copyright: © Copyright 1974 American Mathematical Society

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