| Autor: |
Aitor Balmaseda, Fabio Di Cosmo, Juan Manuel Pérez-Pardo |
| Jazyk: |
angličtina |
| Rok vydání: |
2019 |
| Předmět: |
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| Zdroj: |
Symmetry, Vol 11, Iss 8, p 1047 (2019) |
| Druh dokumentu: |
article |
| ISSN: |
2073-8994 |
| DOI: |
10.3390/sym11081047 |
| Popis: |
An analysis of the invariance properties of self-adjoint extensions of symmetric operators under the action of a group of symmetries is presented. For a given group G, criteria for the existence of G-invariant self-adjoint extensions of the Laplace−Beltrami operator over a Riemannian manifold are illustrated and critically revisited. These criteria are employed for characterising self-adjoint extensions of the Laplace−Beltrami operator on an infinite set of intervals, Ω , constituting a quantum circuit, which are invariant under a given action of the group Z . A study of the different unitary representations of the group Z on the space of square integrable functions on Ω is performed and the corresponding Z -invariant self-adjoint extensions of the Laplace−Beltrami operator are introduced. The study and characterisation of the invariance properties allows for the determination of the spectrum and generalised eigenfunctions in particular examples. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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