Invariance of a Shift-Invariant Space in Several Variables
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 Rd, and prove the existence of shift-invariant spaces that are ex...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2011 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/14911 |
| Acceso en línea: | http://hdl.handle.net/11336/14911 |
| Access Level: | acceso abierto |
| Palabra clave: | FIBERS RANGE FUNCTIONS SHIFT-INVARIANT SPACE TRANSLATION INVARIANT SPACE https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | 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 Rd, 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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