Linear Independence of Finite Gabor Systems Determined by Behavior at Infinity
Journal of Geometric Analysis
Gabor systems, HRT conjecture, Hardy fields, Kronecker's theorem
We prove that the HRT (Heil, Ramanathan, and Topiwala) conjecture holds for finite Gabor systems generated by square-integrable functions with certain behavior at infinity. These functions include functions ultimately decaying faster than any exponential function, as well as square-integrable functions ultimately analytic and whose germs are in a Hardy field that is closed under translations. Two classes of the latter type of functions are the set of square-integrable logarithmico-exponential functions and the set of square-integrable Pfaffian functions. We also prove the HRT conjecture for certain finite Gabor systems generated by positive functions.
Benedetto, Johnny J. and Bourouihiya, Abdelkrim, "Linear Independence of Finite Gabor Systems Determined by Behavior at Infinity" (2015). Mathematics Faculty Articles. 70.