Resolvents of Bochner Laplacians in the semiclassical limit
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- September 2023
- DOI:
- 10.48550/arXiv.2309.04955
- arXiv:
- arXiv:2309.04955
- Bibcode:
- 2023arXiv230904955C
- Keywords:
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- Mathematics - Differential Geometry;
- Mathematics - Analysis of PDEs;
- Mathematics - Spectral Theory