Semiclassical functional calculus on nilpotent Lie groups and their compact nilmanifolds
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| Format: | Preprint |
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2024
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| _version_ | 1866912019049873408 |
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| author | Fischer, Véronique Mikkelsen, Søren |
| author_facet | Fischer, Véronique Mikkelsen, Søren |
| contents | In this paper, we show that the semiclassical calculus recently developed on nilpotent Lie groups and nilmanifolds include the functional calculus of suitable subelliptic operators. Moreover, we obtain Weyl laws for these operators. Amongst these operators are sub-Laplacians in horizontal divergence form perturbed with a potential and their generalisations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_05520 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Semiclassical functional calculus on nilpotent Lie groups and their compact nilmanifolds Fischer, Véronique Mikkelsen, Søren Analysis of PDEs Mathematical Physics Functional Analysis Representation Theory 43A85, 43A32, 22E30, 35H20, 35P20, 81Q10 In this paper, we show that the semiclassical calculus recently developed on nilpotent Lie groups and nilmanifolds include the functional calculus of suitable subelliptic operators. Moreover, we obtain Weyl laws for these operators. Amongst these operators are sub-Laplacians in horizontal divergence form perturbed with a potential and their generalisations. |
| title | Semiclassical functional calculus on nilpotent Lie groups and their compact nilmanifolds |
| topic | Analysis of PDEs Mathematical Physics Functional Analysis Representation Theory 43A85, 43A32, 22E30, 35H20, 35P20, 81Q10 |
| url | https://arxiv.org/abs/2409.05520 |