Title: Gabor Frames for Quasicrystals
Speaker: Michael Kreisel (UMD)
Franz Luef's work demonstrates how projective modules over noncommutative tori provide structures which tie together many results on lattice Gabor frames. We shall show that a similar situation occurs in the case of Gabor frames coming from quasicrystals, where there are corresponding operator algebras and projective modules. In particular, there always exist multiwindow Gabor frames for a quasicrystal. The dimensions of the modules end up being equal to the frame measure as defined by Balan, Casazza, Heil, and Landau. The structure of the commutants also suggest that there are generalizations of Janssen's representation to quasicrystalline Gabor frames.