AI 中文总结
本文构造了密度无界的离散集Λ，其计数测度的傅里叶变换为含δ₀''项的缓增分布，并用此构造出具有紧支撑函数对实数直线的无界密度平移铺砌。
AI 中文摘要
本文中，我们给出了一个密度无界的离散集Λ⊂ℝ的简单显式例子，其计数测度的傅里叶变换δ̂_Λ是形如cδ₀'' + μ的缓增分布，其中μ是由三个算术级数的并集支撑的离散测度。该例子随后被用于构造一个具有紧支撑的函数对实数直线的无界密度平移铺砌。
英文摘要
In this note we provide a simple explicit example of a discrete set $Λ\subset\mathbb{R}$ of unbounded density such that the Fourier transform of its counting measure $\widehatδ_Λ$ is a tempered distribution of the form $cδ_0'' + μ$ where $μ$ is a discrete measure supported by a union of three arithmetic progressions. This example is then used to construct a translational tiling of unbounded density of the real line by a function with compact support.
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