Extensions of vector-valued functions with preservation of derivatives

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• 作者：Martin Koc^a ; ^{martin.koc@rsj.com} ; Jan Kolá ; ř^b ; ^c ; ^{kolar@math.cas.cz}
• 关键词：Vector-valued differentiable functions ; Extensions ; Strict differentiability ; Partitions of unity
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 May 2017
• 年：2017
• 卷：449
• 期：1
• 页码：343-367
• 全文大小：606 K
• 卷排序：449

文摘

Let X and Y   be Banach or normed linear spaces and F⊂XF⊂X a closed set. We apply our recent extension theorem for vector-valued Baire one functions to obtain an extension theorem for vector-valued functions f:F→Yf:F→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 (point-wise) Lipschitz property and (for finite dimensional domain X) preservation of strict differentiability and global (eventually local) Lipschitz continuity. This work depends on the paper Extensions of vector-valued Baire one functions with preservation of points of continuity (Koc and Kolář (2016) [20]).