非阿基米德域上函数的逼近性和整体可微性
Approximate and global differentiability of functions over non-archimedean fields
摘要：
本文主要研究非阿基米德无穷域上具有非平凡赋值的函数的逼近可微性、整体可微性和沿曲线可微性。考虑具有零和非零特征的域。利用偏差商定义了可微函数空间。近似可微性研究相对于实值措施。证明了这三类可微性之间的关系定理。研究了这类函数扩张的相关问题。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
