Abstract
Based on an approach of de Branges and the theory of entire functions, we prove two results pertaining to the Bernstein approximation problem, one concerning analytic perturbations of quasianalytic weights and the other dealing with density of polynomials in spaces with nonsymmetric weights. We improve earlier results of V. P. Gurarii and A. Volberg, giving a more complete answer to a question posed by L. Ehrenpreis and S. N. Mergelyan.
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