Berezin-Toeplitz quantization and its kernel expansion

Abstract

We survey recent results about the asymptotic expansion of Toeplitz operators and their kernels, as well as Berezin-Toeplitz quantization. We deal in particular with calculation of the first coefficients of these expansions.

34 pages

Cited by in corpus (11)

• Asymptotics of spectral function of lower energy forms and Bergman kernel of semi-positive and big line bundles
• Exponential Estimate for the asymptotics of Bergman kernels
• Berezin-Toeplitz quantization for lower energy forms
• Semi-classical properties of Berezin--Toeplitz operators with $\cC^k$--\,symbol
• Generalized Bergman kernels on symplectic manifolds of bounded geometry
• Scaling asymptotics of Szego kernels under commuting Hamiltonian actions
• Equivariant Asymptotics of Szegö kernels under Hamiltonian $U(2)$ actions
• Equivariant Asymptotics of Szegö kernels under Hamiltonian $SU(2)$-action
• On the coefficients of the asymptotic expansion of the kernel of Berezin-Toeplitz quantization
• Berezin-Toeplitz quantization for eigenstates of the Bochner-Laplacian on symplectic manifolds
• Equivariant fixed point formulae and Toeplitz operators under Hamiltonian torus actions