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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On $C^ m$ rational approximation
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by Joan Verdera PDF
Proc. Amer. Math. Soc. 97 (1986), 621-625 Request permission

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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Additional Information
  • © Copyright 1986 American Mathematical Society
  • 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