Invariance of a Shift-Invariant Space

By Akram Aldroubi, Carlos Cabrelli, Christopher Heil, Keri Kornelson, Ursula Molter. 2008

47 citations recorded by the source corpus.

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.

View Paper: https://www.semanticscholar.org/paper/fbb022d2fccd259380c0a6c6767b21e3777dfe33

Citations in the corpus

• Subspaces of L2(G) invariant under translation by an abelian subgroup (2014, unknown): “ng by Kamyabi Gol and Raisi Tousi [31]; Cabrelli and Paternostro [12]; and Bownik and Ross [11]. Attacking from another direction, the \extra" invariance of an invariant subspace, the authors of [1, 3, 4, 39] describe H-TI spaces under the assumption that Hcontains a nice subgoup K. All of thes”