On the Three Balls Inequality for Discrete Schr{ö}dinger Operators on Certain Periodic Graphs

Abstract

We investigate quantitative unique continuation properties for discrete magnetic Schr{ö}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.