Bergman kernels for Paley–Wiener spaces and Nazarov’s proof of the Bourgain–Milman theorem

A Bergman kernel proof of the Kawamata subadjunction theorem

The main purpose of the following article is to give a proof of Y. Kawa-mata's celebrated subadjunction theorem in the spirit of our previous work on Bergman kernels. We will use two main ingredients : an L 2 m –extension theorem of Ohsawa-Takegoshi type (which is also a new result) and a more complete version of our former results. §0 Introduction Let X be a projective manifold and let Θ be a ...

Asymptotic Behaviour of Reproducing Kernels of Weighted Bergman Spaces

Let Ω be a domain in Cn, F a nonnegative and G a positive function on Ω such that 1/G is locally bounded, Aα the space of all holomorphic functions on Ω square-integrable with respect to the measure FαGdλ, where dλ is the 2n-dimensional Lebesgue measure, and Kα(x, y) the reproducing kernel for Aα. It has been known for a long time that in some special situations (such as on bounded symmetric do...

Double Integral Characterization for Bergman Spaces

‎In this paper we characterize Bergman spaces with‎ ‎respect to double integral of the functions $|f(z)‎ ‎-f(w)|/|z-w|$,‎ ‎$|f(z)‎ -‎f(w)|/rho(z,w)$ and $|f(z)‎ ‎-f(w)|/beta(z,w)$,‎ ‎where $rho$ and $beta$ are the pseudo-hyperbolic and hyperbolic metrics‎. ‎We prove some necessary and sufficient conditions that implies a function to be...

Reproducing kernels , Bergman kernels , Poisson kernels

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...