Invariance of a Shift-Invariant Space in Several Variables

Details Invariance of a Shift-Invariant Space in Several Variables Invariance of a Shift-Invariant Space in Several Variables

2009-05-12

arxiv.org/abs/0905.1933v2

Mathematics

Classical Analysis and ODEs

20 pages, Some corrections were added. To appear in Complex Analysis and Operator Theory

Scientific paper

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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