LCA群上平移不变空间的额外不变性
Extra Invariance of Shift-Invariant Spaces on LCA Groups
摘要：
设G是LCA群，K是G的闭子群. L^2（G）的闭子空间称为K-不变子空间，如果它在K的元素的平移下是不变的。设H是G中的可数一致格，M是G中包含H的任意闭子群。本文研究了H-不变空间是M-不变空间的充要条件。作为我们结果的一个结果，我们证明了对于G的每个包含格H的闭子群M，存在一个H-不变空间S，它恰好是M-不变的。也就是说，S在任何其他包含M的子群M'下都不是不变的。我们也得到了估计的支持傅里叶变换的生成元的H-不变空间，其M-不变性。
英文摘要：
Let G be an LCA group and K a closed subgroup of G. A closed subspace of L^2(G) is called K-invariant if it is invariant under translations by elements of K. Assume now that H is a countable uniform lattice in G and M is any closed subgroup of G containing H. In this article we study necessary and sufficient conditions for an H-invariant space to be M-invariant. As a consequence of our results we prove that for each closed subgroup M of G containing the lattice H, there exists an H-invariant space S that is exactly M-invariant. That is, S is not invariant under any other subgroup M' containing M. We also obtain estimates on the support of the Fourier transform of the generators of the H-invariant space, related to its M-invariance.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
