Approximate and global differentiability of functions over non-archimedean fields
S. V. Ludkovsky
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.
Create a lesson
Related papers
Weak type (1,1) bound criterion for maximal truncated singular integral operators with rough kernels
Xudong Lai, Lingxin Xu
Discrete intermediate dimensions: endpoints, spectra and quasi-isometric invariance
Jinjun Li, Lifeng Xi, Shuqin Zhang
Weighted norm inequalities for operators with new Muckenhoupt type weights in the Bessel setting and applications
Yongming Wen, Huoxiong Wu
Compactness and essential norms for two-weight fractional Riesz transforms on curves
Ji Li, Chun-Yen Shen, Chaojie Wen et al.
A proof of Kahane's conjecture in the Wiener algebra
Przemysław Ohrysko
Multiple non-collision periodic solutions for second order singular differential systems with parameters
Laura María Fernández-Pardo, Jorge Rodríguez-López