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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.10867 |
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| _version_ | 1866910875363835904 |
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| author | Milatovic, Ognjen |
| author_facet | Milatovic, Ognjen |
| contents | We show that if we start from a symmetric lower semi-bounded Schrödinger operator $\mathcal{H}$ on finitely supported functions on a discrete weighted graph (satisfying certain conditions), apply the Friedrichs construction to get a self-adjoint extension $H$, and then perturb $H$ by a non-negative function $W$, then the resulting form-sum $H\widetilde{+}W$ coincides with the Friedrichs extension of $\mathcal{H}+W$. Additionally, we consider a non-negative perturbation of an essentially self-adjoint lower semi-bounded Schrödinger operator $H$ on a discrete weighted graph. We show that, under certain conditions on the graph and the perturbation, the essential self-adjointness of $H$ remains stable under the given perturbation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_10867 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On two properties of positively perturbed discrete Schrödinger operators Milatovic, Ognjen Spectral Theory Analysis of PDEs 35J10, 39A12, 47B25 We show that if we start from a symmetric lower semi-bounded Schrödinger operator $\mathcal{H}$ on finitely supported functions on a discrete weighted graph (satisfying certain conditions), apply the Friedrichs construction to get a self-adjoint extension $H$, and then perturb $H$ by a non-negative function $W$, then the resulting form-sum $H\widetilde{+}W$ coincides with the Friedrichs extension of $\mathcal{H}+W$. Additionally, we consider a non-negative perturbation of an essentially self-adjoint lower semi-bounded Schrödinger operator $H$ on a discrete weighted graph. We show that, under certain conditions on the graph and the perturbation, the essential self-adjointness of $H$ remains stable under the given perturbation. |
| title | On two properties of positively perturbed discrete Schrödinger operators |
| topic | Spectral Theory Analysis of PDEs 35J10, 39A12, 47B25 |
| url | https://arxiv.org/abs/2503.10867 |