Approximate and global differentiability of functions over non-archimedean fields
Classical Analysis and ODEs
2010-03-16 v1
Abstract
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.
Cite
@article{arxiv.math/0608724,
title = {Approximate and global differentiability of functions over non-archimedean fields},
author = {S. V. Ludkovsky},
journal= {arXiv preprint arXiv:math/0608724},
year = {2010}
}
Comments
29 pages