Group Riesz and frame sequences: the Bracket and the Gramian
Tóm tắt
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 all previous Bracket characterizations of Riesz and frame sequences generated by a single element under a unitary representation.
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