Title: The Duality Principle for Gabor Frames
Speaker: Mads Jakobsen (Technical University of Denmark)
In 1995 three groups of authors, Daubechies, Landau and Landau; Ron and Shen; and Janssen simultaneously announced the, so-called, duality principle for Gabor frames: a Gabor system is a frame for L2(R) if, and only if, the Gabor system with the adjoint lattice is a Riesz sequence in L2(R). Interestingly, the techniques to prove the result are very different in these three papers. Moreover, the articles are quite technical and difficult to understand and in most literature one simply states the result and refers the reader to the original papers for a proof. In my talk I will provide a complete proof of the duality principle. On the way we will make use of the Janssen representation for the Gabor frame operator, use the short-time Fourier transform and exploit properties of the modulation space M^1, also known as Feichtingers algebra. Most importantly, the proof I will present immediately carries over to the more general case of non-separable Gabor systems on locally compact abelian groups.