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arXiv · 1608.02767

Group Riesz and Frame Sequences: The Bracket and the Gramian

Davide Barbieri·Eugenio Hernandez·Victoria Paternostro
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Abstract

Given a discrete group and a unitary representation on a Hilbert space $\mathcal{H}$, we prove that the notions of operator Bracket map and Gramian coincide on a dense set of $\mathcal{H}$. As a consequence, combining this result with known frame theory, we can recover in a simple way all previous Bracket characterizations of Riesz and frame sequences generated by a single element under a unitary representation.

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Davide Barbieri, Eugenio Hernandez, Victoria Paternostro. 2016-08-09. Group Riesz and Frame Sequences: The Bracket and the Gramian. https://arxiv.org/abs/1608.02767

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