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arXiv · 2303.06694

On the structure of the diffusion distance induced by the fractional dyadic Laplacian

María Florencia Acosta·Hugo Aimar·Ivana Gómez·Federico Morana
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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 ${t>0}$, the diffusion metric is a function of the dyadic distance, given in $\mathbb{R}^+$ by $\delta(x,y) = \inf\{|I|: I \text{ is a dyadic interval containing } x \text{ and } y\}$. Even if these functions of $\delta$ are not equivalent to $\delta$, the families of balls are the same, to wit, the dyadic intervals.

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María Florencia Acosta, Hugo Aimar, Ivana Gómez, Federico Morana. 2023-03-12. On the structure of the diffusion distance induced by the fractional dyadic Laplacian. https://doi.org/10.7494/opmath.2024.44.2.157

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