Approximation of Dirac operators with $\boldsymbolδ$-shell potentials in the norm resolvent sense, I. Qualitative results
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866912460646121472 |
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| author | Behrndt, Jussi Holzmann, Markus Stelzer, Christian |
| author_facet | Behrndt, Jussi Holzmann, Markus Stelzer, Christian |
| contents | In this paper the approximation of Dirac operators with general $δ$-shell potentials supported on $C^2$-curves in $\mathbb{R}^2$ or $C^2$-surfaces in $\mathbb{R}^3$, which may be bounded or unbounded, is studied. It is shown under suitable conditions on the weight of the $δ$-interaction that a family of Dirac operators with regular, squeezed potentials converges in the norm resolvent sense to the Dirac operator with the $δ$-shell interaction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_13344 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Approximation of Dirac operators with $\boldsymbolδ$-shell potentials in the norm resolvent sense, I. Qualitative results Behrndt, Jussi Holzmann, Markus Stelzer, Christian Spectral Theory In this paper the approximation of Dirac operators with general $δ$-shell potentials supported on $C^2$-curves in $\mathbb{R}^2$ or $C^2$-surfaces in $\mathbb{R}^3$, which may be bounded or unbounded, is studied. It is shown under suitable conditions on the weight of the $δ$-interaction that a family of Dirac operators with regular, squeezed potentials converges in the norm resolvent sense to the Dirac operator with the $δ$-shell interaction. |
| title | Approximation of Dirac operators with $\boldsymbolδ$-shell potentials in the norm resolvent sense, I. Qualitative results |
| topic | Spectral Theory |
| url | https://arxiv.org/abs/2308.13344 |