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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On $ C\sp m$ rational approximation


Author: Joan Verdera
Journal: Proc. Amer. Math. Soc. 97 (1986), 621-625
MSC: Primary 30E10
MathSciNet review: 845976
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Abstract: Let $ X \subset {\bf {C}}$ be compact and let $ f$ be a compactly supported function in $ {C^m}({\bf {C}})$, $ 0 < m \in {\bf {Z}}$, such that $ \partial f/\partial \bar z$ vanishes on $ X$ up to order $ m - 1$. We prove that $ f$ can be approximated in $ {C^m}({\bf {C}})$ by a sequence of functions which are holomorphic in neighborhoods of $ X$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0845976-6
PII: S 0002-9939(1986)0845976-6
Article copyright: © Copyright 1986 American Mathematical Society