Pseudo-differential calculus on homogeneous trees
Spectral Theory
2018-03-28 v1 Mathematical Physics
math.MP
Abstract
In the objective of studying concentration and oscillation properties of eigenfunctions of the discrete Laplacian on regular graphs, we construct a pseudo-differential calculus on homogeneous trees, their universal covers. We define symbol classes and associated operators. We prove that these operators are bounded on L^2 and give adjoint and product formulas. Finally we compute the symbol of the commutator of a pseudo-differential operator with the Laplacian.
Cite
@article{arxiv.1302.5387,
title = {Pseudo-differential calculus on homogeneous trees},
author = {Etienne Le Masson},
journal= {arXiv preprint arXiv:1302.5387},
year = {2018}
}