Approximation of Analytic Functions on Compact Sets and Bernstein's Inequality

M. S. Baouendi, C. Goulaouic
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