Inter model sets in $\mathbb R^d$ are model sets
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866916381239279616 |
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| author | Richard, Christoph Strungaru, Nicolae |
| author_facet | Richard, Christoph Strungaru, Nicolae |
| contents | We show that any translate of a model set is a model set in some modified cut-and-project scheme. Restricting to Euclidean direct space, we show that any translate of an inter model set is a model set in some modified cut-and-project scheme with second countable internal space. In both cases, the window in the modified cut-and-project scheme inherits the topological and measure-theoretic properties of the original window. Our results hold in fact for a class beyond inter model sets, which we call almost model sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_01439 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Inter model sets in $\mathbb R^d$ are model sets Richard, Christoph Strungaru, Nicolae Mathematical Physics We show that any translate of a model set is a model set in some modified cut-and-project scheme. Restricting to Euclidean direct space, we show that any translate of an inter model set is a model set in some modified cut-and-project scheme with second countable internal space. In both cases, the window in the modified cut-and-project scheme inherits the topological and measure-theoretic properties of the original window. Our results hold in fact for a class beyond inter model sets, which we call almost model sets. |
| title | Inter model sets in $\mathbb R^d$ are model sets |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2211.01439 |