An analysis of non-selfadjoint first-order differential operators with non-local point interactions
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912224003489792 |
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| author | Fischbacher, Christoph Paraiso, Danie Povey-Rowe, Chloe Zimmerman, Brady |
| author_facet | Fischbacher, Christoph Paraiso, Danie Povey-Rowe, Chloe Zimmerman, Brady |
| contents | We study the spectra of non-selfadjoint first-order operators on the interval with non-local point interactions, formally given by ${i\partial_x+V+k\langle δ,\cdot\rangle}$. We give precise estimates on the location of the eigenvalues on the complex plane and prove that the root vectors of these operators form Riesz bases of $L^2(0,2π)$. Under the additional assumption that the operator is maximally dissipative, we prove that it can have at most one real eigenvalue, and given any $λ\in\mathbb{R}$, we explicitly construct the unique operator realization such that $λ$ is in its spectrum. We also investigate the time-evolution generated by these maximally dissipative operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11278 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An analysis of non-selfadjoint first-order differential operators with non-local point interactions Fischbacher, Christoph Paraiso, Danie Povey-Rowe, Chloe Zimmerman, Brady Spectral Theory Functional Analysis Primary: 47B28, 34B10, 34L05, 34L10, Secondary: 30D99, 47B44, 47E05 We study the spectra of non-selfadjoint first-order operators on the interval with non-local point interactions, formally given by ${i\partial_x+V+k\langle δ,\cdot\rangle}$. We give precise estimates on the location of the eigenvalues on the complex plane and prove that the root vectors of these operators form Riesz bases of $L^2(0,2π)$. Under the additional assumption that the operator is maximally dissipative, we prove that it can have at most one real eigenvalue, and given any $λ\in\mathbb{R}$, we explicitly construct the unique operator realization such that $λ$ is in its spectrum. We also investigate the time-evolution generated by these maximally dissipative operators. |
| title | An analysis of non-selfadjoint first-order differential operators with non-local point interactions |
| topic | Spectral Theory Functional Analysis Primary: 47B28, 34B10, 34L05, 34L10, Secondary: 30D99, 47B44, 47E05 |
| url | https://arxiv.org/abs/2501.11278 |