期刊
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
卷 145, 期 4, 页码 1739-1745出版社
AMER MATHEMATICAL SOC
DOI: 10.1090/proc/13358
关键词
Gabor frames; projective unitary representations; time-frequency lattice; von Neumann algebras
资金
- NSF [DMS-1106934, DMS-1403400]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1403400] Funding Source: National Science Foundation
It is well known that a Gabor representation on L-2(R-d ) admits a frame generator h is an element of L-2(R-d) if and only if the associated lattice satisfies the Beurling density condition, which in turn can be characterized as the trace condition for the associated von Neumann algebra. It happens that this trace condition is also necessary for any projective unitary representation of a countable group to admit a frame vector. However, it is no longer sufficient for general representations, and in particular not sufficient for Gabor representations when they are restricted to proper time-frequency invariant subspaces. In this short note we show that the condition is also sufficient for a large class of projective unitary representations, which implies that the Gabor density theorem is valid for subspace representations in the case of irrational types of lattices.
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