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...

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Bibliographic Details
Published inThe Journal of fourier analysis and applications Vol. 16; no. 1; pp. 60 - 75
Main Authors Aldroubi, Akram, Cabrelli, Carlos, Heil, Christopher, Kornelson, Keri, Molter, Ursula
Format Journal Article
LanguageEnglish
Published Boston SP Birkhäuser Verlag Boston 01.02.2010
Subjects
Abstract Harmonic Analysis
Approximations and Expansions
Fourier Analysis
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Partial Differential Equations
Signal,Image and Speech Processing
Dimension function
Frames
Range function
42C40
46C99
Fiber space
Shift-invariant space
Gramian operator
Translation-invariant space
42C15
Riesz basis
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Summary: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.
ISSN:1069-5869
1531-5851
DOI:10.1007/s00041-009-9068-y