论文标题
可区分P-ADIC函数的某些属性
Some properties of differentiable p-adic functions
论文作者
论文摘要
在本文中，使用Linability理论中的工具，我们区分了$ p $ - adiC可分解函数的某些子集。 Specifically, we show that the following sets of functions are large enough to contain an infinite dimensional algebraic structure: (i) continuously differentiable but not strictly differentiable functions, (ii) strictly differentiable functions of order $r$ but not strictly differentiable of order $r+1$, (iii) strictly differentiable functions with zero derivative that are not Lipschitzian of any order $α>1$, (iv) differentiable具有无界导数的功能，以及（v）连续函数，这些函数在完整的HAAR度量方面是可区分的，但在其补充具有基数的连续性方面并非可区分。
In this paper, using the tools from the lineability theory, we distinguish certain subsets of $p$-adic differentiable functions. Specifically, we show that the following sets of functions are large enough to contain an infinite dimensional algebraic structure: (i) continuously differentiable but not strictly differentiable functions, (ii) strictly differentiable functions of order $r$ but not strictly differentiable of order $r+1$, (iii) strictly differentiable functions with zero derivative that are not Lipschitzian of any order $α>1$, (iv) differentiable functions with unbounded derivative, and (v) continuous functions that are differentiable on a full set with respect to the Haar measure but not differentiable on its complement having cardinality the continuum.
