On the Three Balls Inequality for Discrete Schr\"odinger Operators on Certain Periodic Graphs
Abstract
We investigate quantitative unique continuation properties for discrete magnetic Schr\"odinger 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.
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