Approximation of analytic functions on compact sets and Bernstein’s inequality
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- by M. S. Baouendi and C. Goulaouic
- Trans. Amer. Math. Soc. 189 (1974), 251-261
- DOI: https://doi.org/10.1090/S0002-9947-1974-0352789-7
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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.References
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Bibliographic Information
- © Copyright 1974 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 189 (1974), 251-261
- MSC: Primary 41A10
- DOI: https://doi.org/10.1090/S0002-9947-1974-0352789-7
- MathSciNet review: 0352789