Compact open spectral sets in Q(p)
Compact open spectral sets in Q(p)
复制标题
Qp 中的紧凑开放光谱集
DOI：
10.1016/j.jfa.2016.08.021
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发表时间：
2016
影响因子：
1.7
通讯作者：
SHI Ruxi
中科院分区：
文献类型：
--
作者：
FAN Aihua;FAN Shilei;SHI Ruxi
本文证明了p-adic数域Qp中的紧致开集是谱集的充要条件是Qp平移平铺，且当且仅当Qp是易于检验的p-齐次的.利用分块性和齐次性刻画了Z/pnZ（p≥ 2素数，n≥ 1整数）中的谱集.此外，我们构造了一类奇异谱测度，其中一些是自相似测度。
In this article, we prove that a compact open set in the field Q p of p-adic numbers is a spectral set if and only if it tiles Q p by translation, and also if and only if it is p-homogeneous which is easy to check. We also characterize spectral sets in Z/p n Z (p≥ 2 prime, n≥ 1 integer) by tiling property and also by homogeneity. Moreover, we construct a class of singular spectral measures in Q p, some of which are self-similar measures.