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.

Full text (pdf)

  1. M. Actis, H. Aimar, Pointwise convergence to the initial data for nonlocal dyadic diffusions, Czechoslovak Math. J. 66 (2016), no. 1, 93-204. https://doi.org/10.1007/s10587-016-0249-y
  2. H. Aimar, I. Gómez, On the Calderón-Zygmund structure of Petermichl's kernel, C.R. Acad. Sci. Paris, Ser. I 356 (2018), no. 5, 509-516. https://doi.org/10.1016/j.crma.2018.04.002
  3. R.R. Coifman, S. Lafon, Diffusion maps, Appl. Comput. Harmon. Anal. 21 (2006), 5-30. https://doi.org/10.1016/j.acha.2006.04.006
  4. R.A. Macías, C. Segovia, Lipschitz functions on spaces of homogenous type, Advances in Mathematics 33 (1979), no. 3, 257-270. https://doi.org/10.1016/0001-8708(79)90012-4
  • 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
  • ORCID iD 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)
  • ORCID iD 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.
Opuscula Mathematica - cover

Cite this article as:
María Florencia Acosta, Hugo Aimar, Ivana Gómez, Federico Morana, On the structure of the diffusion distance induced by the fractional dyadic Laplacian, Opuscula Math. 44, no. 2 (2024), 157-165, https://doi.org/10.7494/OpMath.2024.44.2.157

Download this article's citation as:
a .bib file (BibTeX),
a .ris file (RefMan),
a .enw file (EndNote)
or export to RefWorks.

We advise you this website uses cookies to allow us to see how the site is used. All data is anonymized.
All recent versions of popular browsers give users a level of control over cookies. Users can set their browsers to accept or reject all, or certain, cookies.