Operator-isomorphism pairs and Zak transform methods for the study of Gabor systems

Abstract

We collect and summarize results on the unitary equivalence of Gabor systems by pairs of unitary operators and global isometries. The methods are then used to study Gabor systems with Hermite functions. We provide new proofs of some known results and an outlook on double over-sampling.

In v1 we wrote "operator-isometry pairs" which was replaced by "operator-isomorphism pairs". Not all of the used transformations of the plane preserve distance (they are area-preserving, though) 4 pages (two columns), 3 figures