Quantization of TF-Lattice invariant operators on elementary LCA groups

H.G. Feichtinger and W. Kozek

Department of Mathematics, University of Vienna, Vienna, Austria
email: fei@tyche.mat.univie.ac.at
homepage: tyche.mat.univie.ac.at/~fei

Elementary locally compact abelian groups G are a natural setup for an abstract view on time-frequency (TF) analysis. The function space Gelfand triple (S_0,L2,S_0')(G) is adapted to the sampling and periodization procedures on the abstract TF-plane Gx{\hat G} and it allows the definition of a generalized Kohn--Nirenberg correspondence for a "harmonic analysis and synthesis" of linear operators. We extend the concept of duality and biorthogonality of Gabor atoms to arbitrary discrete subgroups of Gx{\hat G} with compact quotient. The setting of elementary LCA groups is not only an extension of standard Gabor analysis but admits a unified formulation for continuous-time, discrete-time, periodic, and multidimensional signals including the case of nonseparable lattices and/or nonseparable atoms.