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The connection between Gabor analysis and noncommutative geometry over noncommutative tori is the starting point for the research in this project. Since it allows us to transfer methods and results from one field to the other to enrich both fields. One of the main goals of this project is to gain a better understanding of the structures in time-frequency analysis, and especially in Gabor analysis, by invoking results on projective modules over operator algebras, the K-theory of operator algebras and Rieffel-Morita equivalence of operator algebras. Furthermore we want to investigate the relation between time-frequency analysis and quantum mechanics from the perspective of operator algebras, in particular our focus is towards deformation quantization and phase-space quantum mechanics.
Department of Mathematics
University of California, Berkeley
970 Evans Hall #3840
CA 94720-3840 USA