Resolvents of Bochner Laplacians in the semiclassical limit

Laurent Charles

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arXiv · 2309.04955

Resolvents of Bochner Laplacians in the semiclassical limit

Laurent Charles

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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.

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Laurent Charles. 2023-09-10. Resolvents of Bochner Laplacians in the semiclassical limit. https://arxiv.org/abs/2309.04955

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