Generalized boundary triples for adjoint pairs with applications to non-self-adjoint Schrödinger operators
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909626082000896 |
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| author | Arnal, Antonio Behrndt, Jussi Holzmann, Markus Siegl, Petr |
| author_facet | Arnal, Antonio Behrndt, Jussi Holzmann, Markus Siegl, Petr |
| contents | We extend the notion of generalized boundary triples and their Weyl functions from extension theory of symmetric operators to adjoint pairs of operators, and we provide criteria on the boundary parameters to induce closed operators with a nonempty resolvent set. The abstract results are applied to Schrödinger operators with complex $L^p$-potentials on bounded and unbounded Lipschitz domains with compact boundaries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_22321 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized boundary triples for adjoint pairs with applications to non-self-adjoint Schrödinger operators Arnal, Antonio Behrndt, Jussi Holzmann, Markus Siegl, Petr Spectral Theory Analysis of PDEs Functional Analysis We extend the notion of generalized boundary triples and their Weyl functions from extension theory of symmetric operators to adjoint pairs of operators, and we provide criteria on the boundary parameters to induce closed operators with a nonempty resolvent set. The abstract results are applied to Schrödinger operators with complex $L^p$-potentials on bounded and unbounded Lipschitz domains with compact boundaries. |
| title | Generalized boundary triples for adjoint pairs with applications to non-self-adjoint Schrödinger operators |
| topic | Spectral Theory Analysis of PDEs Functional Analysis |
| url | https://arxiv.org/abs/2505.22321 |