A remark on the absence of eigenvalues in continuous spectra for discrete Schrödinger operators on periodic lattices
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917983311364096 |
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| author | Ando, Kazunori Isozaki, Hiroshi Morioka, Hisashi |
| author_facet | Ando, Kazunori Isozaki, Hiroshi Morioka, Hisashi |
| contents | We prove a Rellich-Vekua type theorem for Schrödinger operators with exponentially decreasing potentials on a class of lattices including square, triangular, hexagonal lattices and their ladders. We also discuss the unique continuation theorem and the non-existence of eigenvalues embedded in the continuous spectrum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_03577 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A remark on the absence of eigenvalues in continuous spectra for discrete Schrödinger operators on periodic lattices Ando, Kazunori Isozaki, Hiroshi Morioka, Hisashi Spectral Theory Mathematical Physics Analysis of PDEs 47A75, 47A40 We prove a Rellich-Vekua type theorem for Schrödinger operators with exponentially decreasing potentials on a class of lattices including square, triangular, hexagonal lattices and their ladders. We also discuss the unique continuation theorem and the non-existence of eigenvalues embedded in the continuous spectrum. |
| title | A remark on the absence of eigenvalues in continuous spectra for discrete Schrödinger operators on periodic lattices |
| topic | Spectral Theory Mathematical Physics Analysis of PDEs 47A75, 47A40 |
| url | https://arxiv.org/abs/2411.03577 |