On links between Gabor Analysis and Noncommutative Geometry
given at strobl05 (23.05.05 10:00)
In the last 25 years Gabor analysis and Noncommutative Geometry have been developed independently from each other. Gabor Analysis on the one side has been highly influenced by signal analysis and other applications. On the other side Noncommutative Geometry was initiated by Alain Connes and his understanding of operator algebras. Only recently Groechenig and Leinert pointed out the relevance of operator algebras for a deeper understanding of central questions of Gabor Analysis. In this talk we want to stress that in noncommutative geometry many notions and results of Gabor analysis have been obtained from a totally different motivation. We will discuss some results of Arveson on the noncommuative "Fourier " transform and the work of Rieffel on Morita equivalence of Gabor analysis and the work of Connes on the construction of projective modules over quantum tori.