Riesz Decompositions for Schr\"odinger Operators on Graphs
Analysis of PDEs
2022-04-13 v1 Mathematical Physics
Functional Analysis
math.MP
Abstract
We study superharmonic functions for Schr\"odinger operators on general weighted graphs. Specifically, we prove two decompositions which both go under the name Riesz decomposition in the literature. The first one decomposes a superharmonic function into a harmonic and a potential part. The second one decomposes a superharmonic function into a sum of superharmonic functions with certain upper bounds given by prescribed superharmonic functions. As application we show a Brelot type theorem.
Cite
@article{arxiv.1905.12474,
title = {Riesz Decompositions for Schr\"odinger Operators on Graphs},
author = {Florian Fischer and Matthias Keller},
journal= {arXiv preprint arXiv:1905.12474},
year = {2022}
}