Toeplitz operators and Hamiltonian torus actions

DOI10.1016/j.jfa.2005.10.011zbMath1099.53059arXivmath/0405128OpenAlexW1975796939MaRDI QIDQ2495368

Laurent Charles

Publication date: 30 June 2006

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0405128

zbMATH Keywords

geometric quantizationFourier integral operatorsemi-classicalmicrolocalsymplectic reduction Toeplitz operator

Mathematics Subject Classification ID

Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) (47B37) Applications of manifolds of mappings to the sciences (58D30) Pseudodifferential and Fourier integral operators on manifolds (58J40) Geometric quantization (53D50)

Related Items

Reduction and coherent states, Semiclassical quantization and spectral limits of ħ-pseudodifferential and Berezin-Toeplitz operators, Berezin-Toeplitz quantization for compact Kähler manifolds. A review of results, Asymptotic Euler-Maclaurin formula over lattice polytopes, Symplectic invariants of semitoric systems and the inverse problem for quantum systems, Higher asymptotics of unitarity in ``quantization commutes with reduction, Singular unitarity in ``quantization commutes with reduction, Spectral asymptotics via the semiclassical Birkhoff normal form, Toeplitz operators on symplectic manifolds, Unitarity in ``Quantization commutes with reduction, \(G\)-invariant Szegő kernel asymptotics and CR reduction, Stability functions, Inverse spectral theory for semiclassical Jaynes-Cummings systems

Cites Work

• General concept of quantization
• Homogeneous quantization and multiplicities of group representations
• Convexity properties of the moment mapping
• Geometric quantization and multiplicities of group representations
• Reduction of symplectic manifolds with symmetry
• The Riemann-Roch theorem for complex V-manifolds
• Symplectic surgery and the Spin\(^c\)-Dirac operator
• Semiclassical spectral estimates for Toeplitz operators
• Fedosov *-products and quantum momentum maps
• Berezin--Toeplitz operators, a semi-classical approach
• The heat kernel Lefschetz fixed point formula for the spin-c dirac operator
• ON A GENERALIZATION OF THE NOTION OF MANIFOLD
• The Spectral Theory of Toeplitz Operators. (AM-99)
• Convexity and Commuting Hamiltonians
• Quasimodes and Bohr-Sommerfeld Conditions for the Toeplitz Operators
• Symplectic reduction and Riemann-Roch formulas for multiplicities
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