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Approximation of Analytic Functions on Compact Sets and Bernstein's Inequality
1974
Transactions of the American Mathematical Society
The characterization of analytic functions defined on a compact set K in Rw 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.
doi:10.2307/1996858
fatcat:m7cb7c2srbelxiuedrbjzcsvzi