On the Three Balls Inequality for Discrete Schr{\"o}dinger Operators on Certain Periodic Graphs
Classical Analysis and ODEs
2025-03-19 v1 Complex Variables
Functional Analysis
Abstract
We investigate quantitative unique continuation properties for discrete magnetic Schr{\"o}dinger operators in certain periodic graphs. This unique continuation property will be quantified through what is known in the literature as a Three Balls Inequality. We are able to extend this inequality to another family of periodic graph which contains the Hexagonal lattice. We also give a sketch of the proof for general star periodic graph.Our proofs are based on Carleman estimates.
Keywords
Cite
@article{arxiv.2503.14038,
title = {On the Three Balls Inequality for Discrete Schr{\"o}dinger Operators on Certain Periodic Graphs},
author = {Philippe Jaming and Yann Bourroux and Aingeru Fernández-Bertolin},
journal= {arXiv preprint arXiv:2503.14038},
year = {2025}
}