多元平移不变空间的不变性
Invariance of a Shift-Invariant Space in Several Variables
摘要：
本文研究了高维移位不变空间的不变性。给出并证明了平移不变空间在$\R^d$的闭子群下不变的几个充要条件，并证明了平移不变空间对每个给定子群精确不变的存在性.作为应用，我们将额外不变性与移位不变空间的生成元的傅里叶变换的支集的大小联系起来。这项工作扩展了最近获得的结果的情况下，一个变量到几个变量。
英文摘要：
In this article we study invariance properties of shift-invariant spaces in higher dimensions. We state and prove several necessary and sufficient conditions for a shift-invariant space to be invariant under a given closed subgroup of $\R^d$, and prove the existence of shift-invariant spaces that are exactly invariant for each given subgroup. As an application we relate the extra invariance to the size of support of the Fourier transform of the generators of the shift-invariant space. This work extends recent results obtained for the case of one variable to several variables.
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