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 Szegö kernel along the diagonal.

Paoletti, R. (2010). Local trace formulae and scaling asymptotics in Toeplitz quantization. INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, 7(3), 379-403 [10.1142/S021988781000435X].

Local trace formulae and scaling asymptotics in Toeplitz quantization

Paoletti, R
2010

Abstract

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 Szegö kernel along the diagonal.
Articolo in rivista - Articolo scientifico
Local asymptotics; Moment map; Scaling limits; Toeplitz operator; Trace formula;
English
2010
7
3
379
403
none
Paoletti, R. (2010). Local trace formulae and scaling asymptotics in Toeplitz quantization. INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, 7(3), 379-403 [10.1142/S021988781000435X].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/8023
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