Invariance of a shift-invariant space

A shift-invariant space is a space of functions that is invariant under integer translations. Such spaces are often used as models for spaces of signals and images in mathematical and engineering applications. This paper characterizes those shift-invariant subspaces S that are also invariant under a...

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Detalles Bibliográficos
Autores: Aldroubi, Akram, Cabrelli, Carlos, Heil, Christopher, Kornelson, Keri, Molter, Ursula Maria
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2010
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/69116
Acceso en línea:http://hdl.handle.net/11336/69116
Access Level:acceso abierto
Palabra clave:DIMENSION FUNCTION
FIBER SPACE
FRAMES
GRAMIAN OPERATOR
RANGE FUNCTION
RIESZ BASIS
SHIFT-INVARIANT SPACE
TRANSLATION-INVARIANT SPACE
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
Descripción
Sumario:A shift-invariant space is a space of functions that is invariant under integer translations. Such spaces are often used as models for spaces of signals and images in mathematical and engineering applications. This paper characterizes those shift-invariant subspaces S that are also invariant under additional (non-integer) translations. For the case of finitely generated spaces, these spaces are characterized in terms of the generators of the space. As a consequence, it is shown that principal shift-invariant spaces with a compactly supported generator cannot be invariant under any non-integer translations.