Extensions of vector-valued functions with preservation of derivatives

Research output: Contribution to journalArticle

Authors

Colleges, School and Institutes

External organisations

  • RSJ a.s.
  • University of Warwick, Warwick, United Kingdom.
  • Institute of Mathematics, Czech Academy of Sciences

Abstract

Let X and Y be Banach or normed linear spaces and F⊂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→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]).

Details

Original languageEnglish
Pages (from-to)343-367
Number of pages25
JournalJournal of Mathematical Analysis and Applications
Volume449
Issue number1
Early online date1 Dec 2016
Publication statusPublished - 1 May 2017

Keywords

  • Extensions, Partitions of unity, Strict differentiability, Vector-valued differentiable functions

ASJC Scopus subject areas