Asymptotic estimates for double-coverings
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866909948361834496 |
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| author | Karagulyan, Grigori A. Karagulyan, Vahe G. |
| author_facet | Karagulyan, Grigori A. Karagulyan, Vahe G. |
| contents | A collection of finite sets $\{A_1, A_2,\ldots, A_{p}\}$ is said to be a double-covering if each $a\in \cup_{k=1}^{p}A_k$ is included in exactly two sets of the collection. For fixed integers $l$ and $p$, let $μ_{l,p}$ be the number of equivalency classes of double-coverings with $\#(A_k)=l$, $k=1,2,\ldots,p$. We characterize the asymptotic behavior of the quantity $μ_{l,p}$ as $p\to \infty$. The results are applied to give an alternative approach to the Bonami-Kiener hypercontraction inequality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_05426 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Asymptotic estimates for double-coverings Karagulyan, Grigori A. Karagulyan, Vahe G. Classical Analysis and ODEs 05A17, 05A20, 05B40, 42C05, 60G42 A collection of finite sets $\{A_1, A_2,\ldots, A_{p}\}$ is said to be a double-covering if each $a\in \cup_{k=1}^{p}A_k$ is included in exactly two sets of the collection. For fixed integers $l$ and $p$, let $μ_{l,p}$ be the number of equivalency classes of double-coverings with $\#(A_k)=l$, $k=1,2,\ldots,p$. We characterize the asymptotic behavior of the quantity $μ_{l,p}$ as $p\to \infty$. The results are applied to give an alternative approach to the Bonami-Kiener hypercontraction inequality. |
| title | Asymptotic estimates for double-coverings |
| topic | Classical Analysis and ODEs 05A17, 05A20, 05B40, 42C05, 60G42 |
| url | https://arxiv.org/abs/2212.05426 |