Spectral pollution in substitution systems
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
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| _version_ | 1866918446006009856 |
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| author | Band, Ram Beckus, Siegfried Pogorzelski, Felix Tenenbaum, Lior |
| author_facet | Band, Ram Beckus, Siegfried Pogorzelski, Felix Tenenbaum, Lior |
| contents | We study spectral properties of Schrödinger operators associated with substitution dynamical systems in higher dimensions. Focusing on periodic approximations generated by iterating substitutions on initial configurations, we analyze how structural defects influence the limiting spectral behavior. In contrast to the one-dimensional setting, we show that such approximations may exhibit significant spectral pollution, including changes in the essential spectrum and the Lebesgue measure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_12637 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Spectral pollution in substitution systems Band, Ram Beckus, Siegfried Pogorzelski, Felix Tenenbaum, Lior Spectral Theory Dynamical Systems We study spectral properties of Schrödinger operators associated with substitution dynamical systems in higher dimensions. Focusing on periodic approximations generated by iterating substitutions on initial configurations, we analyze how structural defects influence the limiting spectral behavior. In contrast to the one-dimensional setting, we show that such approximations may exhibit significant spectral pollution, including changes in the essential spectrum and the Lebesgue measure. |
| title | Spectral pollution in substitution systems |
| topic | Spectral Theory Dynamical Systems |
| url | https://arxiv.org/abs/2604.12637 |