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arXiv · 1206.1657

Linear independence of time-frequency translates of functions with faster than exponential decay

Marcin Bownik·Darrin Speegle
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Abstract

We establish the linear independence of time-frequency translates for functions $f$ having one sided decay $\lim_{x\to \infty} |f(x)| e^{cx \log x} = 0$ for all $c>0$. We also prove such results for functions with faster than exponential decay, i.e., $\lim_{x\to \infty} |f(x)| e^{cx} = 0$ for all $c>0$, under some additional restrictions.

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Marcin Bownik, Darrin Speegle. 2012-06-08. Linear independence of time-frequency translates of functions with faster than exponential decay. https://doi.org/10.1112/blms%2Fbds119

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