Invariance of a Shift-Invariant Space in Several Variables |
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Authors: | Magal�� Anastasio Carlos Cabrelli Victoria Paternostro |
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Institution: | 1. Departamento de Matem??tica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabell??n I, 1428, Buenos Aires, Argentina 2. CONICET, Consejo Nacional de Investigaciones Cient??ficas y T??cnicas, Buenos Aires, Argentina
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Abstract: | 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
\mathbb Rd{\mathbb {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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Keywords: | |
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