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arXiv · 1211.0337

Linear Independence of Finite Gabor Systems Determined by Behavior at Infinity

John J. Benedetto·Abdelkrim Bourouihiya
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Abstract

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. 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.

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John J. Benedetto, Abdelkrim Bourouihiya. 2012-11-02. Linear Independence of Finite Gabor Systems Determined by Behavior at Infinity. https://arxiv.org/abs/1211.0337

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