Projective modules over noncommutative tori are multi-window Gabor frames for modulation spaces
نویسندگان
چکیده
منابع مشابه
Projective Modules over Noncommutative Tori Are Multi-window Gabor Frames for Modulation Spaces
In the present investigation we link noncommutative geometry over noncommutative tori with Gabor analysis, where the first has its roots in operator algebras and the second in time-frequency analysis. We are therefore in the position to invoke modern methods of operator algebras, e.g. topological stable rank of Banach algebras, to exploit the deeper properties of Gabor frames. Furthermore, we a...
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Representations of the celebrated Heisenberg commutation relations in quantum mechanics (and their exponentiated versions) form the starting point for a number of basic constructions, both in mathematics and mathematical physics (geometric quantization, quantum tori, classical and quantum theta functions) and signal analysis (Gabor analysis). In this paper we will try to bridge the two communit...
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The non-commutative tori provide probably the most accessible interesting examples of non-commutative differentiable manifolds. We can identify an ordinary n-torus rn with its algebra, C(rn), of continuous complex-valued functions under pointwise multiplication. But C(rn) is the universal C*-algebra generated by n commuting unitary operators. By definition, [15, 16, 50], a non-commutative n-tor...
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We point out a connection between Gabor analysis and noncommutative analysis. Especially, the strong Morita equivalence of noncommutative tori appears as underlying setting for Gabor analysis, since the construction of equivalence bimodules for noncommutative tori has a natural formulation in the notions of Gabor analysis. As an application we show that Feichtinger’s algebra is such an equivale...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2009
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2009.06.001