On 𝐶^{𝑚} rational approximation

Verdera, Joan

doi:10.1090/S0002-9939-1986-0845976-6

On $C^ m$ rational approximation
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by Joan Verdera

Proc. Amer. Math. Soc. 97 (1986), 621-625

DOI: https://doi.org/10.1090/S0002-9939-1986-0845976-6

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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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