Local trace formulae and scaling asymptotics in Toeplitz quantization

Details Local trace formulae and scaling asymptotics in Toeplitz quantization Local trace formulae and scaling asymptotics in Toeplitz quantization

2009-07-24

arxiv.org/abs/0907.4225v1

Mathematics

Spectral Theory

Scientific paper

A trace formula for Toeplitz operators was proved by Boutet de Monvel and Guillemin in the setting of general Toeplitz structures. Here we give a local version of this result for a class of Toeplitz operators related to continuous groups of symmetries on quantizable compact symplectic manifolds. The local trace formula involves certain scaling asymptotics along the clean fixed locus of the Hamiltonian flow of the symbol, reminiscent of the scaling asymptotics of the equivariant components of the Szeg\"o kernel along the diagonal.

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