Mathematical Research Letters

Volume 17 (2010)

Number 4

Linear independence of time frequency translates for special configurations

Pages: 761 – 779

DOI: http://dx.doi.org/10.4310/MRL.2010.v17.n4.a14

Author

Ciprian Demeter (Indiana University, Bloomington IN)

Abstract

We prove that for any 4 points in the plane that belong to 2 parallel lines, there is no linear dependence between the associated time-frequency translates of any nontrivial Schwartz function. If mild Diophantine properties are satisfied, we also prove linear independence in the category of $L^2(\R)$ functions

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