Bergman kernels and symplectic reduction

Ja n 20 05 GENERALIZED BERGMAN KERNELS ON SYMPLECTIC MANIFOLDS

We study the near diagonal asymptotic expansion of the generalized Bergman kernel of the renormalized Bochner-Laplacian on high tensor powers of a positive line bundle over a compact symplectic manifold. We show how to compute the coefficients of the expansion by recurrence and give a closed formula for the first two of them. As consequence, we calculate the density of states function of the Bo...

Reproducing kernels , Bergman kernels , Poisson kernels

m at h . D G ] 2 4 Ju l 2 00 6 BERGMAN KERNELS AND SYMPLECTIC REDUCTION

We generalize several recent results concerning the asymptotic expansions of Bergman kernels to the framework of geometric quantization and establish an asymptotic symplectic identification property. More precisely, we study the asymptotic expansion of the G-invariant Bergman kernel of the spinc Dirac operator associated with high tensor powers of a positive line bundle on a symplectic manifold...

Weighted Bergman Kernels and Quantization

Let Ω be a bounded pseudoconvex domain in C N , φ, ψ two positive functions on Ω such that − logψ,− log φ are plurisubharmonic, z ∈ Ω a point at which − log φ is smooth and strictly plurisubharmonic, and M a nonnegative integer. We show that as k → ∞, the Bergman kernels with respect to the weights φkψM have an asymptotic expansion KφkψM (x, y) = kN πNφ(x, y)kψ(x, y)M ∞ ∑ j=0 bj(x, y) k −j , b0...

WEIGHTED BERGMAN KERNELS AND QUANTIZATIONMiroslav