Quantization on filtered manifolds
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910129609244672 |
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| author | Kammerer, Clotilde Fermanian Fischer, Véronique Flynn, Steven |
| author_facet | Kammerer, Clotilde Fermanian Fischer, Véronique Flynn, Steven |
| contents | In this article, we develop a pseudodifferential calculus on a general filtered manifold M . The symbols are fields of operators $σ$(x, $π$) parametrised by x $\in$ M and the unitary dual G x M of the osculating Lie group G x M . We define classes of symbols and a local quantization formula associated to a local frame adapted to the filtration. We prove that the collection of operators on M coinciding locally with the quantization of symbols enjoys the essential properties of a pseudodifferential calculus: composition, adjoint, parametrices, continuity on adapted Sobolev spaces. Moreover, we show that the polyhomogeneous subcalculus coincides with the calculus constructed by van Erp and Yuncken via groupoids. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_17448 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantization on filtered manifolds Kammerer, Clotilde Fermanian Fischer, Véronique Flynn, Steven Functional Analysis In this article, we develop a pseudodifferential calculus on a general filtered manifold M . The symbols are fields of operators $σ$(x, $π$) parametrised by x $\in$ M and the unitary dual G x M of the osculating Lie group G x M . We define classes of symbols and a local quantization formula associated to a local frame adapted to the filtration. We prove that the collection of operators on M coinciding locally with the quantization of symbols enjoys the essential properties of a pseudodifferential calculus: composition, adjoint, parametrices, continuity on adapted Sobolev spaces. Moreover, we show that the polyhomogeneous subcalculus coincides with the calculus constructed by van Erp and Yuncken via groupoids. |
| title | Quantization on filtered manifolds |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2412.17448 |