Clusters of resonances for a non-selfadjoint multichannel discrete Schrödinger operator
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866909753060360192 |
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| author | Assal, Marouane Bourget, Olivier Miranda, Pablo Sambou, Diomba |
| author_facet | Assal, Marouane Bourget, Olivier Miranda, Pablo Sambou, Diomba |
| contents | We study the distribution of resonances for discrete Hamiltonians of the form $H_0+V$ near the thresholds of the spectrum of $H_0$. Here, the unperturbed operator $H_0$ is a multichannel Laplace type operator on $\ell^2(\mathbb Z; \mathbb C^N) \cong \ell^2(\mathbb Z)\otimes \mathbb C^N$ and $V$ is a non-selfadjoint compact perturbation. We compute the exact number of resonances and give a precise description on their location in clusters around some special points in the complex plane. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_01352 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Clusters of resonances for a non-selfadjoint multichannel discrete Schrödinger operator Assal, Marouane Bourget, Olivier Miranda, Pablo Sambou, Diomba Mathematical Physics Analysis of PDEs Spectral Theory We study the distribution of resonances for discrete Hamiltonians of the form $H_0+V$ near the thresholds of the spectrum of $H_0$. Here, the unperturbed operator $H_0$ is a multichannel Laplace type operator on $\ell^2(\mathbb Z; \mathbb C^N) \cong \ell^2(\mathbb Z)\otimes \mathbb C^N$ and $V$ is a non-selfadjoint compact perturbation. We compute the exact number of resonances and give a precise description on their location in clusters around some special points in the complex plane. |
| title | Clusters of resonances for a non-selfadjoint multichannel discrete Schrödinger operator |
| topic | Mathematical Physics Analysis of PDEs Spectral Theory |
| url | https://arxiv.org/abs/2203.01352 |