论文标题
关于翻译平铺的傅立叶分析标准的示例
An example concerning Fourier analytic criteria for translational tiling
论文作者
论文摘要
众所周知，在l^1（\ Mathbb {r}^d）$中的函数$ f \，其沿晶格$λ$形成瓷砖的函数可以完全表征其傅立叶变换的零集。我们构建了一个离散集$λ\ subset \ mathbb {r} $（整数的少量扰动）的示例，对于这种函数而言，这是不可能的：有两个函数$ f，g \ in l^1（\ mathbb {r}）$，其傅立叶变换的同一$ f +是$ f +。
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.
