Comparison of some notions of Ck-maps in multi-variable non-archimedian analysis
Glöckner, Helge
Bull. Belg. Math. Soc. Simon Stevin, Tome 13 (2007) no. 5, p. 877-904 / Harvested from Project Euclid
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Various definitions of $C^k$-maps on open subsets of finite-dimensional vector spaces over a complete valued field have been proposed in the literature. We show that the $C^k$-maps considered by Schikhof and De Smedt coincide with those of Bertram, Glöckner and Neeb. By contrast, Ludkovsky's $C^k$-maps need not be $C^k$ in the former sense, at least in positive characteristic. We also compare various types of Hölder differentiable maps on finite-dimensional and metrizable spaces.
Publié le : 2007-12-14
Classification:  Non-archimedian analysis,  differentiable map,  partial difference quotient,  directional difference quotient,  differentiability property,  weak differentiability,  26E30,  26E20,  46A16,  46G05,  46S10 
@article{1197908901,
     author = {Gl\"ockner, Helge},
     title = {Comparison of some notions of C<sup>k</sup>-maps in multi-variable non-archimedian analysis},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {13},
     number = {5},
     year = {2007},
     pages = { 877-904},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1197908901}
}

Glöckner, Helge. Comparison of some notions of Ck-maps in multi-variable non-archimedian analysis. Bull. Belg. Math. Soc. Simon Stevin, Tome 13 (2007) no. 5, pp.  877-904. http://gdmltest.u-ga.fr/item/1197908901/