Openness of the frame set on the hyperbolas

Aleksei Kulikov

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arXiv · 2404.00585

Openness of the frame set on the hyperbolas

Aleksei Kulikov

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Abstract

We prove that for the functions of the form $g(x) = h(x) + \frac{C}{x+i}$, where $h$ belongs to the continuous Wiener algebra $W_0$, the intersection of the frame set $\mathcal{F}_g$ with every hyperbola $\{\alpha, \beta > 0 \mid \alpha\beta = c\}$ is open in the relative topology. In particular, this applies to all rational functions $g$.

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Aleksei Kulikov. 2024-03-31. Openness of the frame set on the hyperbolas. https://arxiv.org/abs/2404.00585

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