LCA群上的移位调制不变空间
Shift-modulation invariant spaces on LCA groups
摘要：
$(K,Λ)$移位调制不变空间是$L^2(G)$的子空间，其通过沿$K$中的元素的平移和通过$Λ$中的元素的调制而不变。这里$G$是一个局部紧阿贝尔群，$K$和$Λ$分别是$G$和对偶群$\hat G$的闭子群。在这篇文章中，我们提供了一个在这种情况下，当$K$和$Λ$是一致格的移位调制不变空间的特征。这推广了以前已知的$L^2(\R^d)$的结果。我们开发了纤维化技术和合适的范围功能，以适应LCA组需要提供所需的表征。
英文摘要：
A $(K,Λ)$ shift-modulation invariant space is a subspace of $L^2(G)$, that is invariant by translations along elements in $K$ and modulations by elements in $Λ$. Here $G$ is a locally compact abelian group, and $K$ and $Λ$ are closed subgroups of $G$ and the dual group $\hat G$, respectively. In this article we provide a characterization of shift-modulation invariant spaces in this general context when $K$ and $Λ$ are uniform lattices. This extends previous results known for $L^2(\R^d)$. We develop fiberization techniques and suitable range functions adapted to LCA groups needed to provide the desired characterization.
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