Resolvents of Bochner Laplacians in the semiclassical limit
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866908296771796992 |
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| author | Charles, Laurent |
| author_facet | Charles, Laurent |
| contents | We introduce a new class of pseudodifferential operators, called Heisenberg semiclassical pseudodifferential operators, to study the space of sections of a power of a line bundle on a compact manifold, in the limit where the power is large. This class contains the Bochner Laplacian associated with a connection of the line bundle, and when the curvature is nondegenerate, its resolvent and some associated spectral projections, including generalized Bergman kernels. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_04955 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Resolvents of Bochner Laplacians in the semiclassical limit Charles, Laurent Differential Geometry Analysis of PDEs Spectral Theory We introduce a new class of pseudodifferential operators, called Heisenberg semiclassical pseudodifferential operators, to study the space of sections of a power of a line bundle on a compact manifold, in the limit where the power is large. This class contains the Bochner Laplacian associated with a connection of the line bundle, and when the curvature is nondegenerate, its resolvent and some associated spectral projections, including generalized Bergman kernels. |
| title | Resolvents of Bochner Laplacians in the semiclassical limit |
| topic | Differential Geometry Analysis of PDEs Spectral Theory |
| url | https://arxiv.org/abs/2309.04955 |