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Scientific article
English

Differentiable extensions of functions

Published inDifferential geometry and its applications, vol. 3, no. 1, p. 71-90
Publication date1993
Abstract

Those functions on arbitrary subsets of Image, which admit smooth extensions to Image, as well as those, which admit k-times differentiable extension having locally Lipschitzian derivatives, are characterized in terms of a simple boundedness condition on the difference quotients. In case of finite order differentiability also a continuous linear extension operator is constructed for the corresponding function spaces even for vector valued functions.

Keywords
  • Extension of functions
  • convenient vector spaces
  • Lipschitz condition
  • difference quotients
  • interpolation
Citation (ISO format)
FROLICHER, Alfred, KRIEGL, Andréas. Differentiable extensions of functions. In: Differential geometry and its applications, 1993, vol. 3, n° 1, p. 71–90. doi: 10.1016/0926-2245(93)90023-T
Identifiers
ISSN of the journal0926-2245
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