Invariance of a Shift-Invariant Space
Functional Analysis
2010-07-07 v3 Classical Analysis and ODEs
Abstract
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.
Cite
@article{arxiv.0804.1597,
title = {Invariance of a Shift-Invariant Space},
author = {Akram Aldroubi and Carlos Cabrelli and Christopher Heil and Keri Kornelson and Ursula Molter},
journal= {arXiv preprint arXiv:0804.1597},
year = {2010}
}
Comments
15 pages