@Article{Acosta2024,
author = "Acosta, María Florencia and Aimar, Hugo and Gómez, Ivana and Morana, Federico",
title = "On the structure of the diffusion distance induced by the fractional dyadic Laplacian",
journal = "Opuscula Math.",
year = "2024",
volume = "44",
number = "2",
pages = "157--165",
doi = "https://doi.org/10.7494/OpMath.2024.44.2.157",
url = "https://doi.org/10.7494/OpMath.2024.44.2.157",
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",
issn = "1232-9274"
}