论文标题
非Archimedean Koksma不平等，变化和傅立叶分析
Non-Archimedean Koksma inequalities, variation, and Fourier analysis
论文作者
论文摘要
我们研究了在非架构的局部领域的整数紧凑环上定义的实现函数的四个不同概念，并重点侧重于具有有限变化的函数的规律性特性，并建立了非Archimedean Koksma不平等。第一个版本的变体是由于泰伯森（Taibleson）造成的，第二版是由于啤酒而引起的，其余两个是新的。泰伯森（Taibleson）的变化是其中最简单的，但它是对不规则性的粗略度量，并且不承认科克斯玛（Koksma）不等式。啤酒的变化可用于证明koksma不平等，但依赖订单且不翻译不变。我们定义了一种新版本的变体，当函数自然扩展到Berkovich Offine Line的某个子树时，可以解释为图理论变化。这种变化是无订单的，翻译不变的，它承认koksma的不平等现象，对于某些自然的例子，它总是比啤酒更明显。最后，我们定义了傅立叶分析变化和相应的Koksma不平等，有时比伯科维奇分析不平等更明显。
We examine four different notions of variation for real-valued functions defined on the compact ring of integers of a non-Archimedean local field, with an emphasis on regularity properties of functions with finite variation, and on establishing non-Archimedean Koksma inequalities. The first version of variation is due to Taibleson, the second due to Beer, and the remaining two are new. Taibleson variation is the simplest of these, but it is a coarse measure of irregularity and it does not admit a Koksma inequality. Beer variation can be used to prove a Koksma inequality, but it is order-dependent and not translation invariant. We define a new version of variation which may be interpreted as the graph-theoretic variation when a function is naturally extended to a certain subtree of the Berkovich affine line. This variation is order-free and translation invariant, and it admits a Koksma inequality which, for a certain natural family of examples, is always sharper than Beer's. Finally, we define a Fourier-analytic variation and a corresponding Koksma inequality which is sometimes sharper than the Berkovich-analytic inequality.
