Extensions of vector-valued functions with preservation of derivatives

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 $f:F\to Y$ 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.

21 pages, 2 figures. Depends on arXiv:1512.03717

References in corpus (2)

• On Baire classification of mappings with values in connected spaces
• Extensions of vector-valued Baire one functions with preservation of points of continuity

Cited by in corpus (1)

• Extensions of vector-valued Baire one functions with preservation of points of continuity