A Proof of the HRT Conjecture for Widely Spaced Sets [article]

Michael Kreisel
2018 arXiv   pre-print
Given f ∈ C_0(R^n) and Λ⊂R^2n a finite set we demonstrate the linear independence of the set of time-frequency translates G(f, Λ) = {π(λ)f}_λ∈Λ when the time coordinates of points in Λ are far apart relative to the decay of f. As a corollary, we prove that for any f ∈ C_0(R^n) and finite Λ⊂R^2n there exist infinitely many dilations D_r such that G(D_rf, Λ) is linearly independent. Furthermore, we prove that G(f, Λ) is linearly independent for functions like f(t) = cos(t)/|t| which have a
more » ... rity and are bounded away from any neighborhood of the singularity.
arXiv:1805.06116v2 fatcat:4vyrphz5ufhexbhmbz76gtupqu