Berezin-Toeplitz quantization on Kaehler manifolds

Abstract

We study the Berezin-Toeplitz quantization on Kaehler manifolds. We explain first how to compute various associated asymptotic expansions, then we compute explicitly the first terms of the expansion of the kernel of the Berezin-Toeplitz operators, and of the composition of two Berezin-Toeplitz operators. As application we estimate the norm of Donaldson's Q-operator.

45 pages, footnote at page 3 and Remark 0.5 added; v.3 is a final update to agree with the published paper

References in corpus (3)

• Toeplitz operators on symplectic manifolds
• Quantisation and the Hessian of Mabuchi energy
• Black holes and balanced metrics

Cited by in corpus (30)

• Quantum Hall effect and Quillen metric
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• Berezin-Toeplitz quantization for lower energy forms
• Quantisation and the Hessian of Mabuchi energy
• Bergman kernels on punctured Riemann surfaces
• Semi-classical properties of Berezin--Toeplitz operators with $\cC^k$--\,symbol
• Remark on the off-diagonal expansion of the Bergman kernel on compact Kähler manifolds
• Quantization of Kähler manifolds
• Rawnsley's $\epsilon$-function on some Hartogs type domains over bounded symmetric domains and its applications
• Uniform Continuity and Quantization on Bounded Symmetric Domains
• Kapranov's $L_{\infty }$ structures, Fedosov's star products, and one-loop exact BV quantizations on Kähler manifolds
• The Asymptotic of the Holomorphic Analytic Torsion Forms
• On the composition of Berezin-Toeplitz operators on symplectic manifolds
• A note on Berezin-Toeplitz quantization of the Laplace operator
• The first terms in the expansion of the Bergman kernel in higher degrees
• Log-scale equidistribution of zeros of quantum ergodic eigensections
• Quantization of the Laplacian operator on vector bundles I
• 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
• The second coefficient of the asymptotic expansion of the Bergman kernel of the Hodge-Dolbeault operator
• The Hessian of quantized Ding functionals and its asymptotic behavior
• Remarks on the canonical metrics on the Cartan-Hartogs domains
• The regular quantizations of certain holomorphic bundles
• On the coefficients of the equivariant Szegő kernel asymptotic expansions
• Geometric quantization and quantum moment maps on coadjoint orbits and Kähler-Einstein manifolds
• On Monge-Ampère volumes of direct images
• On the approximation of functions on a Hodge manifold
• Bergman kernel asymptotics for singular metrics on punctured Riemann surfaces
• Balanced metrics on the Fock-Bargmann-Hartogs domains
• The first terms in the expansion of the Bergman kernel in higher degrees: mixed curvature case