p-进域上的笛卡尔积中的谱集和tiles

Spectral sets and tiles in Cartesian products over the p-adic fields

证明了p-进域上的向量空间中的两个可测集合Ω1??■和Ω2??■的笛卡尔积Ω1×Ω2平移地tile乘积空间?■×?■当且仅当其tile相应的空间.同时,对谱集也研究了类似的问题.

In this paper,we prove that the Cartesian productΩ1×Ω2 of two measurable setsΩ1??■andΩ2??■tile the product space?■×?■by translations if and only if they tile the corresponding space by translations.We also consider the similar problem for spectral sets.