Eigenvalue bounds for Schrödinger operators on quantum graphs with $δ$-coupling conditions
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909617360994304 |
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| author | Cao, Duc Hoang |
| author_facet | Cao, Duc Hoang |
| contents | We prove sharp upper bounds for eigenvalues of Schrödinger operators on quantum graphs with $δ$-coupling (also known as Robin) conditions at all vertices. The bounds depend on the geometry of the graph, on the potential, and the strength of the couplings, and as the coupling strengths grow, the dependence on the topology gets weaker, answering a question of Rohleder and Seifert. We obtain those bounds via the variational characterisation, comparing with appropriate linear combinations of eigenfunctions with Dirichlet and Neumann vertex conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_09235 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Eigenvalue bounds for Schrödinger operators on quantum graphs with $δ$-coupling conditions Cao, Duc Hoang Spectral Theory Classical Analysis and ODEs 34B45, 34L05, 34L40, 81Q35 We prove sharp upper bounds for eigenvalues of Schrödinger operators on quantum graphs with $δ$-coupling (also known as Robin) conditions at all vertices. The bounds depend on the geometry of the graph, on the potential, and the strength of the couplings, and as the coupling strengths grow, the dependence on the topology gets weaker, answering a question of Rohleder and Seifert. We obtain those bounds via the variational characterisation, comparing with appropriate linear combinations of eigenfunctions with Dirichlet and Neumann vertex conditions. |
| title | Eigenvalue bounds for Schrödinger operators on quantum graphs with $δ$-coupling conditions |
| topic | Spectral Theory Classical Analysis and ODEs 34B45, 34L05, 34L40, 81Q35 |
| url | https://arxiv.org/abs/2503.09235 |