关于平移铺砌的傅里叶解析准则的一个例子
An example concerning Fourier analytic criteria for translational tiling
AI总结：
本文构造了一个离散集Λ（整数的小扰动）的反例，证明存在傅里叶变换零集相同但平移铺砌性质不同的函数，表明此类傅里叶解析准则无法完全刻画该集合的铺砌特性。
摘要：
众所周知，沿格点Λ平移后能形成铺砌的函数f∈L^1(R^d)，可通过其傅里叶变换的零集完全刻画。我们构造了一个离散集Λ⊂R（整数的一个小扰动）的例子，对此无法进行此类刻画：存在两个函数f,g∈L^1(R)，其傅里叶变换具有相同的零集，但f+Λ是铺砌而g+Λ不是。
英文摘要：
It is well-known that the functions $f \in L^1(\mathbb{R}^d)$ whose translates along a lattice $Λ$ form a tiling, can be completely characterized in terms of the zero set of their Fourier transform. We construct an example of a discrete set $Λ\subset \mathbb{R}$ (a small perturbation of the integers) for which no characterization of this kind is possible: there are two functions $f, g \in L^1(\mathbb{R})$ whose Fourier transforms have the same set of zeros, but such that $f + Λ$ is a tiling while $g + Λ$ is not.
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。
