Analytic capacity and approximation problems

Author:
A. M. Davie

Journal:
Trans. Amer. Math. Soc. **171** (1972), 409-444

MSC:
Primary 30A82

MathSciNet review:
0350009

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Abstract | References | Similar Articles | Additional Information

Abstract: We consider some problems concerning analytic capacity as a set function, which are relevant to approximation problems for analytic functions on plane sets. In particular we consider the question of semiadditivity of capacity. We obtain positive results in some special cases and give applications to approximation theory. In general we establish some equivalences among various versions of the semiadditivity question and certain questions in approximation theory.

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DOI:
https://doi.org/10.1090/S0002-9947-1972-0350009-9

Keywords:
Analytic capacity,
uniform approximation,
bounded approximation,
negligible set

Article copyright:
© Copyright 1972
American Mathematical Society