多面体上的傅里叶分析简介
A friendly introduction to Fourier analysis on polytopes
摘要：
这本书是对多面体和圆锥体的傅里叶分析的新生领域的介绍。这些方法的应用数量正在迅速增长，因此邀请学生和专业人士到该领域是合适的。在这些技术的众多应用中，我们选择关注以下主题：（a）多面体的傅里叶变换公式（b）数的几何中的Minkowski和Siegel定理（c）通过多面体的平移的欧几里得空间的拼接和多重拼接（d）计算多面体的离散体积，这是连续体积的组合近似（e）球面填充，和他们的包装密度（f）迭代的发散定理，给新的配方的傅里叶变换的多面体，与应用（g）香农采样，在几个变量（h）更多的主题，在经典的数的几何我们假设熟悉线性代数，一些微积分和无穷级数。在整个过程中，我们通过提供许多例子和练习来温和地介绍主题，因此本书非常适合作为课程或自学。
英文摘要：
This book is an introduction to the nascent field of Fourier analysis on polytopes, and cones. There is a rapidly growing number of applications of these methods, so it is appropriate to invite students, as well as professionals, to the field. Of the many applications of these techniques, we have chosen to focus on the following topics: (a) Formulations for the Fourier transform of a polytope (b) Minkowski and Siegel's theorems in the geometry of numbers (c) Tilings and multi-tilings of Euclidean space by translations of a polytope (d) Computing discrete volumes of polytopes, which are combinatorial approximations to the continuous volume (e) Sphere packings, and their packing density (f) Iterating the divergence theorem to give new formulations for the Fourier transform of a polytope, with applications (g) Shannon sampling, in several variables (h) More topics in the classical geometry of numbers We assume familiarity with Linear Algebra, with some Calculus and infinite series. Throughout, we introduce the topics gently, by giving many examples and exercises, so that this book is ideally suited for a course, or for self-study.
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。
