TY  - JOUR
ID  - Acosta2024
LB  - Acosta2024
AU  - Acosta, María Florencia
AU  - Aimar, Hugo
AU  - Gómez, Ivana
AU  - Morana, Federico
TI  - On the structure of the diffusion distance induced by the fractional dyadic Laplacian
ST  - On the structure of the diffusion distance induced by the fractional dyadic Laplacian
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2024
VL  - 44
IS  - 2
SP  - 157
EP  - 165
DO  - https://doi.org/10.7494/OpMath.2024.44.2.157
UR  - https://doi.org/10.7494/OpMath.2024.44.2.157
AB  - 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.
KW  - diffusion metrics
KW  - dyadic diffusion
SN  - 1232-9274
ER  -