scholarly journals Uniform Extendibility of the Bergman Kernel for Generalized Minimal Balls

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Jong-Do Park
Keyword(s):  
Bergman Kernel ◽  
Convex Domains ◽  
Reinhardt Domains ◽  
Nonsmooth Boundary

We consider a class of convex domains which contains non-Reinhardt domains with nonsmooth boundary. We show that the domains of this class satisfy the conditionQ.

scholarly journals The Zeros of the Bergman Kernel for Some Reinhardt Domains

2016 ◽  
Vol 2016 ◽  
pp. 1-9
Author(s):  
Jong-Do Park
Keyword(s):  
Bergman Kernel ◽  
Bernoulli Numbers ◽  
Complete Characterization ◽  
Stirling Number ◽  
Real Polynomial ◽  
Reinhardt Domains ◽  
Exponential Generating Function ◽  
Existence Of Zeros ◽  
Positive Integers

We consider the Reinhardt domainDn={(ζ,z)∈C×Cn:|ζ|2<(1-|z1|2)⋯(1-|zn|2)}.We express the explicit closed form of the Bergman kernel forDnusing the exponential generating function for the Stirling number of the second kind. As an application, we show that the Bergman kernelKnforDnhas zeros if and only ifn≥3. The study of the zeros ofKnis reduced to some real polynomial with coefficients which are related to Bernoulli numbers. This result is a complete characterization of the existence of zeros of the Bergman kernel forDnfor all positive integersn.

ON DISCONTINUITY OF THE BERGMAN KERNEL FUNCTION

1999 ◽  
Vol 10 (07) ◽  
pp. 825-832
Author(s):  
KLAS DIEDERICH ◽  
GREGOR HERBORT
Keyword(s):  
Finite Type ◽  
Kernel Function ◽  
Real Line ◽  
Bergman Kernel ◽  
Pseudoconvex Domain ◽  
Convex Domains ◽  
Bergman Kernel Function ◽  
Finite Type Domains

Let [Formula: see text] be a Ck-smoothly (with k≥1) bounded pseudoconvex domain and [Formula: see text] denote its Bergman kernel function. In this article the question is investigated, whether the function [Formula: see text] is continuous up to the boundary in the topology of the extended real line [Formula: see text]. We give two counterexamples: one in the class of finite type domains with k = ∞ and one in the class of convex domains with k = 1.

scholarly journals Estimates for the Bergman kernel and metric of convex domains in Cn

2003 ◽  
Vol 81 (1) ◽  
pp. 73-78 ◽  
Author(s):  
Nikolai Nikolov ◽  
Peter Pflug
Keyword(s):  
Bergman Kernel ◽  
Convex Domains
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