Stability of shifts, interpolation, and crystalline measures
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915464640200704 |
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| author | Ulanovskii, Alexander Zlotnikov, Ilya |
| author_facet | Ulanovskii, Alexander Zlotnikov, Ilya |
| contents | Let $V^p_Γ(\mathcal{G}),1\leq p\leq\infty,$ be the quasi shift-invariant space generated by $Γ$-shifts of a function $\mathcal{G}$, where $Γ\subset\mathbb{R}$ is a separated set. For several large families of generators $\mathcal{G}$, we present necessary and sufficient conditions on $Γ$ that imply that the $Γ$-shifts of $\mathcal{G}$ form an unconditional basis for $V^p_Γ(\mathcal{G})$. The connection between this property, interpolation, universal interpolation, and crystalline measures is discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_08682 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stability of shifts, interpolation, and crystalline measures Ulanovskii, Alexander Zlotnikov, Ilya Functional Analysis Classical Analysis and ODEs 42B10, 46B15, 52C23 Let $V^p_Γ(\mathcal{G}),1\leq p\leq\infty,$ be the quasi shift-invariant space generated by $Γ$-shifts of a function $\mathcal{G}$, where $Γ\subset\mathbb{R}$ is a separated set. For several large families of generators $\mathcal{G}$, we present necessary and sufficient conditions on $Γ$ that imply that the $Γ$-shifts of $\mathcal{G}$ form an unconditional basis for $V^p_Γ(\mathcal{G})$. The connection between this property, interpolation, universal interpolation, and crystalline measures is discussed. |
| title | Stability of shifts, interpolation, and crystalline measures |
| topic | Functional Analysis Classical Analysis and ODEs 42B10, 46B15, 52C23 |
| url | https://arxiv.org/abs/2410.08682 |