On the Three Balls Inequality for Discrete Schr{ö}dinger Operators on Certain Periodic Graphs
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908273197711360 |
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| author | Jaming, Philippe Bourroux, Yann Fernández-Bertolin, Aingeru |
| author_facet | Jaming, Philippe Bourroux, Yann Fernández-Bertolin, Aingeru |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_14038 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Three Balls Inequality for Discrete Schr{ö}dinger Operators on Certain Periodic Graphs Jaming, Philippe Bourroux, Yann Fernández-Bertolin, Aingeru Classical Analysis and ODEs Complex Variables Functional Analysis 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. |
| title | On the Three Balls Inequality for Discrete Schr{ö}dinger Operators on Certain Periodic Graphs |
| topic | Classical Analysis and ODEs Complex Variables Functional Analysis |
| url | https://arxiv.org/abs/2503.14038 |