On asymptotic expansions of generalized Bergman kernels on symplectic manifolds

Kordyukov, Yu.

doi:10.1090/spmj/1542

On asymptotic expansions of generalized Bergman kernels on symplectic manifolds
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by Yu. A. Kordyukov
Translated by: the author

St. Petersburg Math. J. 30 (2019), 267-283

DOI: https://doi.org/10.1090/spmj/1542

Published electronically: February 14, 2019

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Abstract:

A full off-diagonal asymptotic expansion is established for the generalized Bergman kernels of the renormalized Bochner Laplacians associated with high tensor powers of a positive line bundle over a compact symplectic manifold. As an application, the algebra of Toeplitz operators on the symplectic manifold associated with the renormalized Bochner Laplacian is constructed.

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