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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

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: 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