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Proceedings of the American Mathematical Society

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

 
 

 

On $C^ m$ rational approximation


Author: Joan Verdera
Journal: Proc. Amer. Math. Soc. 97 (1986), 621-625
MSC: Primary 30E10
DOI: https://doi.org/10.1090/S0002-9939-1986-0845976-6
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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Article copyright: © Copyright 1986 American Mathematical Society