Toeplitz operators on quantized compact symplectic manifolds were introduced by Guillemin and Boutet de Monvel, who studied their spectral asymptotics in analogy with the theory developed by Duistermaat, Guillemin, and H\"{o}rmander for pseudodifferential operators. In this survey, we review some recent results concerning eigenfunction asymptotics in this context, largely based on the microlocal description of Szeg\"{o} kernels by Boutet de Monvel and Sj\"{o}strand, and its revisitation and generalization to the almost complex symplectic category by Shiffman and Zelditch. For simplicity, the exposition is restricted to the complex projective setting.

Paoletti, R. (2017). Spectral and eigenfunction asymptotics in Toeplitz quantization. In D. Angella, C. Medori, A. Tomassini (a cura di), Complex and Symplectic Geometry (pp. 179-190). Cham : Springer International Publishing [10.1007/978-3-319-62914-8_14].

Spectral and eigenfunction asymptotics in Toeplitz quantization

Paoletti, R
2017

Abstract

Toeplitz operators on quantized compact symplectic manifolds were introduced by Guillemin and Boutet de Monvel, who studied their spectral asymptotics in analogy with the theory developed by Duistermaat, Guillemin, and H\"{o}rmander for pseudodifferential operators. In this survey, we review some recent results concerning eigenfunction asymptotics in this context, largely based on the microlocal description of Szeg\"{o} kernels by Boutet de Monvel and Sj\"{o}strand, and its revisitation and generalization to the almost complex symplectic category by Shiffman and Zelditch. For simplicity, the exposition is restricted to the complex projective setting.
Capitolo o saggio
Spectral asymptotics, eigenfunction concentration, Hamiltonian flows, geometric quantization, spectral projectors, trace formula
English
Complex and Symplectic Geometry
Angella, D; Medori, C; Tomassini, A
2017
978-3-319-62913-1
21
Springer International Publishing
179
190
Paoletti, R. (2017). Spectral and eigenfunction asymptotics in Toeplitz quantization. In D. Angella, C. Medori, A. Tomassini (a cura di), Complex and Symplectic Geometry (pp. 179-190). Cham : Springer International Publishing [10.1007/978-3-319-62914-8_14].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/184449
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