Invariance of a shift invariance space

A. ALDROUBI, C. CABRELLI, C. HEIL, K KORNELSON, U. MOLTER

JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS

Birkhauser

Lugar: Boston, US; Año: 2010 vol. 16 p. 60 - 75

1069-5869

A shift-invariant space is a space of functions that is invariant under in- teger 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) trans- lations. 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 un- der any non-integer translations.