Linear Independence of Finite Gabor Systems

Abstract

This chapter is an introduction to an open conjecture in time-frequency analysis on the linear independence of a finite set of time-frequency shifts of a given L 2 function. Background and motivation for the conjecture are provided in the form of a survey of related ideas, results, and open problems in frames, Gabor systems, and other aspects of time-frequency analysis, especially those related to independence. The partial results that are known to hold for the conjecture are also presented and discussed.