On Modulation and Translation Invariant Operators and the Heisenberg Module
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915318774890496 |
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| author | Lamando, Arvin McNulty, Henry |
| author_facet | Lamando, Arvin McNulty, Henry |
| contents | We investigate spaces of operators which are invariant under translations or modulations by lattices in phase space. The natural connection to the Heisenberg module is considered, giving results on the characterisation of such operators as limits of finite--rank operators. Discrete representations of these operators in terms of elementary objects and the composition calculus are given. Different quantisation schemes are discussed with respect to the results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_09119 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Modulation and Translation Invariant Operators and the Heisenberg Module Lamando, Arvin McNulty, Henry Functional Analysis Operator Algebras 47G30, 47B10, 47B35, 43A15, 46L08, 46L65 We investigate spaces of operators which are invariant under translations or modulations by lattices in phase space. The natural connection to the Heisenberg module is considered, giving results on the characterisation of such operators as limits of finite--rank operators. Discrete representations of these operators in terms of elementary objects and the composition calculus are given. Different quantisation schemes are discussed with respect to the results. |
| title | On Modulation and Translation Invariant Operators and the Heisenberg Module |
| topic | Functional Analysis Operator Algebras 47G30, 47B10, 47B35, 43A15, 46L08, 46L65 |
| url | https://arxiv.org/abs/2406.09119 |