Opuscula Math. 44, no. 2 (2024), 157-165
https://doi.org/10.7494/OpMath.2024.44.2.157
Opuscula Mathematica
On the structure of the diffusion distance induced by the fractional dyadic Laplacian
María Florencia Acosta
Hugo Aimar
Ivana Gómez
Federico Morana
Abstract. 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 \(t\gt 0\), the diffusion metric is a function of the dyadic distance, given in \(\mathbb{R}^+\) by \(\delta(x,y) = \inf\{|I|\colon I \text{ is a dyadic interval containing } x \text{ and } y\}\). Even if these functions of \(\delta\) are not equivalent to \(\delta\), the families of balls are the same, to wit, the dyadic intervals.
Keywords: diffusion metrics, dyadic diffusion.
Mathematics Subject Classification: 54E35, 35K08.
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- María Florencia Acosta
- Instituto de Matemática Aplicada del Litoral "Dra. Eleonor Harboure", UNL, CONICET, CCT CONICET Santa Fe, Predio "Dr. Alberto Cassano", Colectora Ruta Nac. 168 km 0, Paraje El Pozo, S3007ABA Santa Fe, Argentina
- Hugo Aimar
https://orcid.org/0000-0003-3829-7738- Instituto de Matemática Aplicada del Litoral "Dra. Eleonor Harboure", UNL, CONICET, CCT CONICET Santa Fe, Predio "Dr. Alberto Cassano", Colectora Ruta Nac. 168 km 0, Paraje El Pozo, S3007ABA Santa Fe, Argentina
- Ivana Gómez (corresponding author)
- https://orcid.org/0000-0003-2921-2392
- Instituto de Matemática Aplicada del Litoral "Dra. Eleonor Harboure", UNL, CONICET, CCT CONICET Santa Fe, Predio "Dr. Alberto Cassano", Colectora Ruta Nac. 168 km 0, Paraje El Pozo, S3007ABA Santa Fe, Argentina
- Federico Morana
- Instituto de Matemática Aplicada del Litoral "Dra. Eleonor Harboure", UNL, CONICET, CCT CONICET Santa Fe, Predio "Dr. Alberto Cassano", Colectora Ruta Nac. 168 km 0, Paraje El Pozo, S3007ABA Santa Fe, Argentina
- Communicated by Vicenţiu D. Rădulescu.
- Received: 2023-03-31.
- Accepted: 2023-11-08.
- Published online: 2024-01-15.
