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Linear Independence of Finite Gabor Systems

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Book cover Harmonic Analysis and Applications

Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

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.

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Heil, C. (2006). Linear Independence of Finite Gabor Systems. In: Heil, C. (eds) Harmonic Analysis and Applications. Applied and Numerical Harmonic Analysis. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4504-7_9

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