Linear independence of time frequency translates for special configurations

Details Linear independence of time frequency translates for special configurations Linear independence of time frequency translates for special configurations

2010-06-03

arxiv.org/abs/1006.0732v1

Mathematics

Classical Analysis and ODEs

19 pages; To appear in Mathematical Research Letters

Scientific paper

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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