Riesz and frame systems generated by unitary actions of discrete groups
By Davide Barbieri, E. Hern'andez, Javier Parcet. 2014
60 citations recorded by the source corpus.
We characterize orthonormal bases, Riesz bases and frames which arise from the action of a countable discrete group on a single element of a given Hilbert space H. As might not be abelian, this is done in terms of a bracket map taking values in the L 1 -space associated to the group von Neumann algebra of . Our result generalizes recent work for LCA groups in [26]. In many cases, the bracket map can be computed in terms of a noncommutative form of the Zak transform.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/0f642b0225fd6ae40a4999c6bc95271498810bda
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In Applied Mathematics
- Marzieh Hasannasab
- Ole W. Christensen
- Armenak Petrosyan
- Carlos Cabrelli
- Akram Aldroubi
- Ursula Molter
- Karlheinz Gröchenig
- Christopher Heil
In Mathematical Physics
- Ole W. Christensen
- Marzieh Hasannasab
- Armenak Petrosyan
- Akram Aldroubi
- Carlos Cabrelli
- Ursula Molter
Citations in the corpus
- Operator Representations of Frames: Boundedness, Duality, and Stability (2017, background): “, the paper [6] and the references therein.”
- Iterative actions of normal operators (2016, background): “For us, the motivation to study the iterative actions of normal operators comes from sampling theory and related topics [2, 9, 21, 29, 31, 5, 6, 18, 37, 38, 16, 15].”