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arXiv · 2303.01948

The HRT conjecture for a class of meromorphic functions

Mostafa Maslouhi·Kasso A. Okoudjou
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Abstract

The HRT conjecture states that any finite collection of time-frequency shifts of a non-zero square-integrable function on the real line is linearly independent. In this paper, we establish the linear independence of finite systems of time-frequency shifts of a non-zero meromorphic function. Consequently, we prove that the conjecture is true for any square-integrable function on $\mathbb{R}$ that can be extended to an analytic function on $\mathbb{C}$ except on finitely many points.

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Mostafa Maslouhi, Kasso A. Okoudjou. 2023-02-28. The HRT conjecture for a class of meromorphic functions. https://arxiv.org/abs/2303.01948

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