Poisson kernel expansions for Schr\"odinger operators on trees
Spectral Theory
2017-08-28 v2 Mathematical Physics
math.MP
Abstract
We study Schr\"odinger operators on trees and construct associated Poisson kernels, in analogy to the laplacian on the unit disc. We show that in the absolutely continuous spectrum, the generalized eigenfunctions of the operator are generated by the Poisson kernel. We use this to define a "Fourier transform", giving a Fourier inversion formula and a Plancherel formula, where the domain of integration runs over the energy parameter and the geometric boundary of the tree.
Keywords
Cite
@article{arxiv.1610.05907,
title = {Poisson kernel expansions for Schr\"odinger operators on trees},
author = {Nalini Anantharaman and Mostafa Sabri},
journal= {arXiv preprint arXiv:1610.05907},
year = {2017}
}
Comments
To appear in Journal of Spectral Theory