Shift Invariant Spaces on LCA Groups
By Carlos Cabrelli, Victoria Paternostro. 2009
121 citations recorded by the source corpus.
In this article we extend the theory of shift-invariant spaces to the context of LCA groups. We introduce the notion of H-invariant space for a countable discrete subgroup H of an LCA group G, and show that the concept of range function and the techniques of fiberization are valid in this context. As a consequence of this generalization we prove characterizations of frames and Riesz bases of these spaces extending previous results, that were known for Rd and the lattice Zd .
Subfields: Applied Mathematics, Radiology, Nuclear Medicine and Imaging
View Paper: https://www.semanticscholar.org/paper/5cc422a46b86b967f6b1b823c889774d57776dce
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In Applied Mathematics
- E. Hern'andez
- Davide Barbieri
- Victoria Paternostro
- Javier Parcet
- Marius Junge
- Quanhua Xu
- Narcisse Randrianantoanina
In Radiology, Nuclear Medicine and Imaging
Citations in the corpus
- Subspaces of L2(G) invariant under translation by an abelian subgroup (2014, unknown): “This program was continued in increasing generality by Cabrelli and Paternostro [9], Kamyabi Gol and Raisi Tousi [28], Currey, Mayeli, and Oussa [12], and Bownik and Ross [8].”
- The Structure of Translation-Invariant Spaces on Locally Compact Abelian Groups (2015, unknown): “Remark 3.1 Our standing hypotheses on G agree exactly with those in Cabrelli and Paternostro [9], as well as in R. A. Kamyabi Gol and R. Raisi Tousi [22–24].”
- Riesz and frame systems generated by unitary actions of discrete groups (2014, background): “The characterization of shift invariant spaces in LCA groups was also addressed in [7], in terms of the range function instead of the bracket map.”
- The Zak transform and the structure of spaces invariant by the action of an LCA group (2014, methodology): “The main results of [5, 7] are a characterization of spaces invariant under translations in terms of range function using fiberization techniques.”