Approximate and global differentiability of functions over non-archimedean fields

Details Approximate and global differentiability of functions over non-archimedean fields Approximate and global differentiability of functions over non-archimedean fields

2006-08-29

arxiv.org/abs/math/0608724v1

J. Mathem. Sci. 2009

Mathematics

Classical Analysis and ODEs

29 pages

Scientific paper

The article is devoted to approximate, global and along curves differentiability of functions over non-archimedean infinite fields with non-trivial valuations. Fields with zero and non-zero characteristics are considered. Spaces of differentiable functions are defined with the help of partial difference quotients. Approximate differentiability is studied relative to real-valued measures. Theorems about relations between these three types of differentiability are proved. Associated problem on extensions of such functions is investigated.

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