Holomorphic Extensions of Whitney Jets |
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Authors: | Rainer Brück Leonhard Frerick |
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Institution: | 1. Fachbereich Mathematik, Universit?t Dortmund, D-44221, Dortmund, Germany 2. Fachbereich Mathematik, Bergische Universit?t Wuppertal, Gau?stra?e 20, D-42097, Wuppertal, Germany
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Abstract: | Let φ be a Whitney jet on a closed set F ? ?. By Whitney’s extension theorem φ can be extended to an infinitely differentiable function f on ? which is real analytic on ? F. The main purpose of this article is to show that f can be chosen in such a way that f¦?F has a holomorphic continuation to the open set (? F) × i? ? ?. In the special case that F is a compact interval or a single point we can even achieve that f¦?F has a holomorphic continuation to all of $\hat {\rm C}\setminus F$ . In particular, this implies an improvement of the well-known theorem of E. Borel. We also investigate the question when such extensions are given by a so-called extension operator. |
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