Gaussian curvature of the Bergman metric with weighted Bergman kernel on the unit disc

Gaussian Curvature of the Bergman Metric with Weighted Bergman Kernel on the Unit Disc

In the paper Gaussian curvature of Bergman metric on the unit disc and the dependence of this curvature on the weight function has been studied.

Composition Operators from the Weighted Bergman Space to the nth Weighted Spaces on the Unit Disc

The Stability of the Bergman Kernel and the Geometry of the Bergman Metric

If D is a bounded open subset of C", the set H = {ƒ: D —> C| ƒ is holomorphic and SD\f\ 2 < +°°} is a separable infinite-dimensional Hubert space relative to the inner product <ƒ, g) = fDfg. The completeness of H can be seen from Cauchy integral estimates. Similar estimates show that for any p E D the functional ƒ H* ƒ(/?),ƒ£ H, is continuous. Thus there is a unique element KD(z, p) E f/ (as a ...

The Bergman Kernel Function

In this note, we point out that a large family of n × n matrix valued kernel functions defined on the unit disc D ⊆ C, which were constructed recently in [9], behave like the familiar Bergman kernel function on D in several different ways. We show that a number of questions involving the multiplication operator on the corresponding Hilbert space of holomorphic functions on D can be answered usi...

On the Asymptotic Expansion of Bergman Kernel

We study the asymptotic of the Bergman kernel of the spin Dirac operator on high tensor powers of a line bundle.