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arXiv · 1602.05750

Extensions of vector-valued functions with preservation of derivatives

Martin Koc·Jan Kolář
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Abstract

Let $X$ and $Y$ be Banach or normed linear spaces and $F\subset X$ a closed set. We apply our recent extension theorem for vector-valued Baire one functions arXiv:1512.03717 to obtain an extension theorem for vector-valued functions $f\colon F\to Y$ with pre-assigned derivatives, with preservation of differentiability (at every point where the pre-assigned derivative is actually a derivative), preservation of continuity, preservation of (pointwise) Lipschitz property and (for finite dimensional domain $X$) preservation of strict differentiability and global (eventually local) Lipschitz continuity.

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Martin Koc, Jan Kolář. 2016-02-18. Extensions of vector-valued functions with preservation of derivatives. https://doi.org/10.1016/j.jmaa.2016.11.080

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