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

Acosta María Florencia, Aimar Hugo, Gómez Ivana, Morana Federico

Opuscula Mathematica

2024

Vol. 44, no. 2

157--165

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 R+ by δ(x, y) = inf {|I| : I is a dyadic interval containing x 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.