Semiclassical analysis and the Agmon-Finsler metric for discrete Schr\'odinger operators
| Autor: | Kameoka, Kentaro |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Communications on Pure and Applied Analysis (2023) |
| Druh dokumentu: | Working Paper |
| Popis: | The Agmon estimate for multi-dimensional discrete Schr\"{o}dinger operators is studied with emphasis on the microlocal analysis on the torus. We first consider the semiclassical setting where semiclassical continuous Schr\"{o}dinger operators are discretized with the mesh width proportional to the semiclassical parameter. Under this setting, the Agmon estimate for eigenfunctions is described by an Agmon metric, which is a Finsler metric rather than a Riemannian metric. Klein-Rosenberger (2008) proved this by a different argument in the case of a potential minimum. We also prove the Agmon estimate and the optimal anisotropic exponential decay of eigenfunctions for discrete Schr\"{o}dinger operators in the non-semiclassical standard setting. Comment: 16 pages |
| Databáze: | arXiv |
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