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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2601.11839 |
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| _version_ | 1866915824089956352 |
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| author | Potter, Tom Taylor, Keith |
| author_facet | Potter, Tom Taylor, Keith |
| contents | For a crystal group $Γ$ in dimension $n$, a closed subspace $\mathcal{V}$ of $L^2(\mathbb{R}^n)$ is called $Γ$--shift invariant if, for every $f\in\mathcal{V}$, the shifts of $f$ by every element of $Γ$ also belong to $\mathcal{V}$. The main purpose of this paper is to provide a characterization of the $Γ$--shift invariant closed subspaces of $L^2(\mathbb{R}^n)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_11839 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Subspaces of $L^2(\mathbb{R}^n)$ Invariant Under Shifts by a Crystal Group Potter, Tom Taylor, Keith Functional Analysis For a crystal group $Γ$ in dimension $n$, a closed subspace $\mathcal{V}$ of $L^2(\mathbb{R}^n)$ is called $Γ$--shift invariant if, for every $f\in\mathcal{V}$, the shifts of $f$ by every element of $Γ$ also belong to $\mathcal{V}$. The main purpose of this paper is to provide a characterization of the $Γ$--shift invariant closed subspaces of $L^2(\mathbb{R}^n)$. |
| title | Subspaces of $L^2(\mathbb{R}^n)$ Invariant Under Shifts by a Crystal Group |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2601.11839 |