Cyclicity in weighted $\ell^p$ spaces
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | LE MANACH, Florian | |
| dc.date.accessioned | 2024-04-04T03:10:48Z | |
| dc.date.available | 2024-04-04T03:10:48Z | |
| dc.date.created | 2017-03-06 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193716 | |
| dc.description.abstractEn | We study the cyclicity in weighted $\ell^p(\mathbb{Z})$ spaces. For $p \geq 1$ and $\beta \geq 0$, let $\ell^p_\beta(\mathbb{Z})$ be the space of sequences $u=(u_n)_{n\in \mathbb{Z}}$ such that $(u_n |n|^{\beta})\in \ell^p(\mathbb{Z}) $. We obtain both necessary conditions and sufficient conditions for $u$ to be cyclic in $\ell^p_\beta(\mathbb{Z})$, in other words, for $ \{(u_{n+k})_{n \in \mathbb{Z}},~ k \in \mathbb{Z} \}$ to span a dense subspace of $\ell^p_\beta(\mathbb{Z})$. The conditions are given in terms of the Hausdorff dimension and the capacity of the zero set of the Fourier transform of $u$. | |
| dc.language.iso | en | |
| dc.subject.en | cyclicity | |
| dc.subject.en | weighted $\ell^p$ spaces | |
| dc.subject.en | capacity | |
| dc.title.en | Cyclicity in weighted $\ell^p$ spaces | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math]/Analyse fonctionnelle [math.FA] | |
| dc.subject.hal | Mathématiques [math]/Analyse classique [math.CA] | |
| dc.identifier.arxiv | 1703.02841 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-01483933 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01483933v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=LE%20MANACH,%20Florian&rft.genre=preprint |
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