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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Bounded limits of analytic functions


Author: A. M. Davie
Journal: Proc. Amer. Math. Soc. 32 (1972), 127-133
MSC: Primary 30A18
DOI: https://doi.org/10.1090/S0002-9939-1972-0293069-1
MathSciNet review: 0293069
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Abstract: Let U be a bounded open plane set, and let f be a bounded analytic function on U, which is the pointwise limit of a bounded sequence $ \{ {f_n}\} $ of uniformly continuous analytic functions. It is shown that one can find another such sequence $ \{ {f'_n}\} $, converging to f, and bounded by the supremum norm of f. A similar result is proved for approximation by rational functions.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0293069-1
Keywords: Bounded open plane set, bounded analytic function, pointwise bounded limit, annihilating measure
Article copyright: © Copyright 1972 American Mathematical Society