Large sets containing no copies of a given infinite sequence
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866909430921035776 |
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| author | Kolountzakis, Mihail N. Papageorgiou, Effie |
| author_facet | Kolountzakis, Mihail N. Papageorgiou, Effie |
| contents | Suppose $a_n$ is a real, nonnegative sequence that does not increase exponentially. For any $p<1$ we contruct a Lebesgue measurable set $E \subseteq \mathbb{R}$ which has measure at least $p$ in any unit interval and which contains no affine copy $\{x+ta_n:\ n\in\mathbb{N}\}$ of the given sequence (for any $x \in \mathbb{R}, t > 0$). We generalize this to higher dimensions and also for some ``non-linear'' copies of the sequence. Our method is probabilistic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_02637 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Large sets containing no copies of a given infinite sequence Kolountzakis, Mihail N. Papageorgiou, Effie Classical Analysis and ODEs 28A80, 05D40 Suppose $a_n$ is a real, nonnegative sequence that does not increase exponentially. For any $p<1$ we contruct a Lebesgue measurable set $E \subseteq \mathbb{R}$ which has measure at least $p$ in any unit interval and which contains no affine copy $\{x+ta_n:\ n\in\mathbb{N}\}$ of the given sequence (for any $x \in \mathbb{R}, t > 0$). We generalize this to higher dimensions and also for some ``non-linear'' copies of the sequence. Our method is probabilistic. |
| title | Large sets containing no copies of a given infinite sequence |
| topic | Classical Analysis and ODEs 28A80, 05D40 |
| url | https://arxiv.org/abs/2208.02637 |