Tiling the field $\mathbb{Q}_p$ of $p$-adic numbers by a function
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866916566140977152 |
|---|---|
| author | Fan, Shilei |
| author_facet | Fan, Shilei |
| contents | This study explores the properties of the function which can tile the field $\mathbb{Q}_p$ of $p$-adic numbers by translation. It is established that functions capable of tiling $\mathbb{Q}_p$ is by translation uniformly locally constancy. As an application, in the field $\mathbb{Q}_p$, we addressed the question posed by H. Leptin and D. Müller, providing the necessary and sufficient conditions for a discrete set to correspond to a uniform partition of unity. The study also connects these tiling properties to the Fuglede conjecture, which states that a measurable set is a tile if and only if it is spectral. The paper concludes by characterizing the structure of tiles in \(\mathbb{Q}_p \times \mathbb{Z}/2\mathbb{Z}\), proving that they are spectral sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_03834 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tiling the field $\mathbb{Q}_p$ of $p$-adic numbers by a function Fan, Shilei Classical Analysis and ODEs 43A99 This study explores the properties of the function which can tile the field $\mathbb{Q}_p$ of $p$-adic numbers by translation. It is established that functions capable of tiling $\mathbb{Q}_p$ is by translation uniformly locally constancy. As an application, in the field $\mathbb{Q}_p$, we addressed the question posed by H. Leptin and D. Müller, providing the necessary and sufficient conditions for a discrete set to correspond to a uniform partition of unity. The study also connects these tiling properties to the Fuglede conjecture, which states that a measurable set is a tile if and only if it is spectral. The paper concludes by characterizing the structure of tiles in \(\mathbb{Q}_p \times \mathbb{Z}/2\mathbb{Z}\), proving that they are spectral sets. |
| title | Tiling the field $\mathbb{Q}_p$ of $p$-adic numbers by a function |
| topic | Classical Analysis and ODEs 43A99 |
| url | https://arxiv.org/abs/2412.03834 |