Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2021
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2107.04760 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929485205471232 |
|---|---|
| author | Pogorzelski, Felix Richard, Christoph Strungaru, Nicolae |
| author_facet | Pogorzelski, Felix Richard, Christoph Strungaru, Nicolae |
| contents | Consider a positive Borel measure on a locally compact group. We define a notion of uniform density for such a measure, which is based on a group invariant introduced by Leptin in 1966. We then restrict to unimodular amenable groups and to translation bounded measures. In that case our density notion coincides with the well-known Beurling density from Fourier analysis, also known as Banach density from dynamical systems theory. We use Leptin densities for a geometric proof of the model set density formula, which expresses the density of a uniform regular model set in terms of the volume of its window, and for a proof of uniform mean almost periodicity of such model sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_04760 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Leptin densities in amenable groups Pogorzelski, Felix Richard, Christoph Strungaru, Nicolae Group Theory Mathematical Physics Functional Analysis Consider a positive Borel measure on a locally compact group. We define a notion of uniform density for such a measure, which is based on a group invariant introduced by Leptin in 1966. We then restrict to unimodular amenable groups and to translation bounded measures. In that case our density notion coincides with the well-known Beurling density from Fourier analysis, also known as Banach density from dynamical systems theory. We use Leptin densities for a geometric proof of the model set density formula, which expresses the density of a uniform regular model set in terms of the volume of its window, and for a proof of uniform mean almost periodicity of such model sets. |
| title | Leptin densities in amenable groups |
| topic | Group Theory Mathematical Physics Functional Analysis |
| url | https://arxiv.org/abs/2107.04760 |