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

Baouendi, M. S.; Goulaouic, C.

doi:10.1090/S0002-9947-1974-0352789-7

Approximation of analytic functions on compact sets and Bernstein’s inequality
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by M. S. Baouendi and C. Goulaouic PDF

Trans. Amer. Math. Soc. 189 (1974), 251-261 Request permission

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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