Completeness of coherent state subsystems for nilpotent Lie groups
Let $G$ be a nilpotent Lie group and let $\pi $ be a coherent state representation of $G$. The interplay between the cyclicity of the restriction $\pi |_{\Gamma }$ to a lattice $\Gamma \le G$ and the completeness of subsystems of coherent states based on a homogeneous $G$-space is considered. In par...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2022-06-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.342/ |
| Summary: | Let $G$ be a nilpotent Lie group and let $\pi $ be a coherent state representation of $G$. The interplay between the cyclicity of the restriction $\pi |_{\Gamma }$ to a lattice $\Gamma \le G$ and the completeness of subsystems of coherent states based on a homogeneous $G$-space is considered. In particular, it is shown that necessary density conditions for Perelomov’s completeness problem can be obtained via density conditions for the cyclicity of $\pi |_{\Gamma }$. |
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| ISSN: | 1778-3569 |