Which perturbations of quasianalytic weights preserve quasianalyticity? How to use de Branges' theorem

Mikhail Sodin

doi:10.1007/BF02787111

Which perturbations of quasianalytic weights preserve quasianalyticity? How to use de Branges' theorem

Mikhail Sodin^*

^*Corresponding author for this work

School of Mathematical Sciences

NASU - B. Verkin Institute for Low Temperature Physics and Engineering

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

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.

Original language	English
Pages (from-to)	293-309
Number of pages	17
Journal	Journal d'Analyse Mathematique
Volume	69
DOIs	https://doi.org/10.1007/BF02787111
State	Published - 1996

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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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AB - 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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Which perturbations of quasianalytic weights preserve quasianalyticity? How to use de Branges' theorem

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