Extensions of vector-valued functions with preservation of derivatives

0469657 - MÚ 2017 RIV US eng J - Journal Article
Koc, M. - Kolář, Jan
Extensions of vector-valued functions with preservation of derivatives.
Journal of Mathematical Analysis and Applications. Roč. 449, č. 1 (2017), s. 343-367. ISSN 0022-247X. E-ISSN 1096-0813
R&D Projects: GA ČR(CZ) GA14-07880S
Institutional support: RVO:67985840
Keywords : vector-valued differentiable functions * extensions * strict differentiability * partitions of unity
OECD category: Pure mathematics
Impact factor: 1.138, year: 2017
http://www.sciencedirect.com/science/article/pii/S0022247X16307703

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]).
Permanent Link: http://hdl.handle.net/11104/0267473