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

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.

References in corpus (1)

• Proof of the HRT conjecture for (2,2) configurations

Cited by in corpus (7)

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• A Proof of the HRT Conjecture for Widely Spaced Sets
• On the Linear Independence of Finite Wavelet Systems Generated by Schwartz Functions or Functions with certain behavior at infinity
• Linear Independence of Time-Frequency Shifts?