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In my talk I am presenting a link between time-frequency analysis and noncommutative geometry. In particular, a connection between the Moyal plane, noncommutative tori and time-frequency analysis. After a brief description of a dictionary between these two areas I am going to explain some consequences for time-frequency analysis and noncommutative geometry such as the construction of projections in the mentioned operator algebras and Gabor frames.

Keywords: modulation spaces - Banach-Gelfand triples - noncommutative tori - Moyal plane - noncommutative geometry - deformation quantization
In my talk I am presenting a link between time-frequency analysis and noncommutative geometry. In particular, a connection between the Moyal plane, noncommutative tori and time-frequency analysis. After a brief description of a dictionary between these two areas I am going to explain some consequences for time-frequency analysis and noncommutative geometry such as the construction of projections in the mentioned operator algebras and Gabor ...

46Fxx ; 46Kxx ; 46S60 ; 81S05 ; 81S10 ; 81S30

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