Openness of the frame set on the hyperbolas
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916186625671168 |
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| author | Kulikov, Aleksei |
| author_facet | Kulikov, Aleksei |
| contents | 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 $\{α, β> 0 \mid αβ= c\}$ is open in the relative topology. In particular, this applies to all rational functions $g$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_00585 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Openness of the frame set on the hyperbolas Kulikov, Aleksei Functional Analysis 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 $\{α, β> 0 \mid αβ= c\}$ is open in the relative topology. In particular, this applies to all rational functions $g$. |
| title | Openness of the frame set on the hyperbolas |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2404.00585 |