On the structure of the diffusion distance induced by the fractional dyadic Laplacian
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866913235340361728 |
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| author | Acosta, María Florencia Aimar, Hugo Gómez, Ivana Morana, Federico |
| author_facet | Acosta, María Florencia Aimar, Hugo Gómez, Ivana Morana, Federico |
| contents | In this note we explore the structure of the diffusion metric of Coifman-Lafon determined by fractional dyadic Laplacians. The main result is that, for each ${t>0}$, the diffusion metric is a function of the dyadic distance, given in $\mathbb{R}^+$ by $δ(x,y) = \inf\{|I|: I \text{ is a dyadic interval containing } x \text{ and } y\}$. Even if these functions of $δ$ are not equivalent to $δ$, the families of balls are the same, to wit, the dyadic intervals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_06694 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the structure of the diffusion distance induced by the fractional dyadic Laplacian Acosta, María Florencia Aimar, Hugo Gómez, Ivana Morana, Federico Analysis of PDEs General Topology 54E35, 35K08 In this note we explore the structure of the diffusion metric of Coifman-Lafon determined by fractional dyadic Laplacians. The main result is that, for each ${t>0}$, the diffusion metric is a function of the dyadic distance, given in $\mathbb{R}^+$ by $δ(x,y) = \inf\{|I|: I \text{ is a dyadic interval containing } x \text{ and } y\}$. Even if these functions of $δ$ are not equivalent to $δ$, the families of balls are the same, to wit, the dyadic intervals. |
| title | On the structure of the diffusion distance induced by the fractional dyadic Laplacian |
| topic | Analysis of PDEs General Topology 54E35, 35K08 |
| url | https://arxiv.org/abs/2303.06694 |