| Autor: |
Dolbeault, Jean, Esteban, Maria J., Séré, Eric |
| Rok vydání: |
2022 |
| Předmět: |
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| Zdroj: |
J. Spectr. Theory 13 (2023), no. 2, pp. 491-524 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.4171/jst/461 |
| Popis: |
We consider a linear symmetric operator in a Hilbert space that is neither bounded from above nor from below, admits a block decomposition corresponding to an orthogonal splitting of the Hilbert space and has a variational gap property associated with the block decomposition. A typical example is the Dirac-Coulomb operator defined on $C^\infty_c(\mathbb R^3\setminus\{0\}, \mathbb C^4)$. In this paper we define a distinguished self-adjoint extension with a spectral gap and characterize its eigenvalues in that gap by a min-max principle. This has been done in the past under technical conditions. Here we use a different, geometric strategy, to achieve that goal by making only minimal assumptions. Our result applied to the Dirac-Coulomb-like Hamitonians covers sign-changing potentials as well as molecules with an arbitrary number of nuclei having atomic numbers less than or equal to 137. |
| Databáze: |
arXiv |
| Externí odkaz: |
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