Sparse finite Gabor frames for operator sampling

Kurzfassung/Abstract

We derive some interesting properties of finite Gabor frames and apply them to the sampling or identification of operators with bandlimited Kohn-Nirenberg symbols, or equivalently those with compactly supported spreading functions. Specifically we use the fact that finite Gabor matrices are full Spark for an open, dense set of window vectors to show the existence of periodically weighted delta trains that identify simultaneously large operator classes. We also show that sparse delta trains exist that identify operator classes for which the spreading support has small measure.