scholarly journals Asymptotic expansion of the Bergman kernel for strictly pseudoconvex complete Reinhardt domains in $\mathbf{C}^2 $

1990 ◽  
Vol 66 (2) ◽  
pp. 39-41 ◽  
Author(s):  
Noriyuki Nakazawa
Keyword(s):  
Asymptotic Expansion ◽  
Bergman Kernel ◽  
Reinhardt Domains

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 Asymptotic Expansion of the Bergman Kernel via Perturbation of the Bargmann–Fock Model

2015 ◽  
Vol 26 (4) ◽  
pp. 2602-2638 ◽  
Author(s):  
Hamid Hezari ◽  
Casey Kelleher ◽  
Shoo Seto ◽  
Hang Xu
Keyword(s):  
Asymptotic Expansion ◽  
Bergman Kernel

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.

scholarly journals THE FIRST COEFFICIENTS OF THE ASYMPTOTIC EXPANSION OF THE BERGMAN KERNEL OF THESpincDIRAC OPERATOR

2006 ◽  
Vol 17 (06) ◽  
pp. 737-759 ◽  
Author(s):  
XIAONAN MA ◽  
GEORGE MARINESCU
Keyword(s):  
Asymptotic Expansion ◽  
Bergman Kernel ◽  
Dirac Operators ◽  
Line Bundles ◽  
Tensor Powers

We establish the existence of the asymptotic expansion of the Bergman kernel associated to the spincDirac operators acting on high tensor powers of line bundles with non-degenerate mixed curvature (negative and positive eigenvalues) by extending [15]. We compute the second coefficient b1in the asymptotic expansion using the method of [24].

scholarly journals On the asymptotic expansion of Bergman kernel

2004 ◽  
Vol 339 (3) ◽  
pp. 193-198 ◽  
Author(s):  
Xianzhe Dai ◽  
Kefeng Liu ◽  
Xiaonan Ma
Keyword(s):  
Asymptotic Expansion ◽  
Bergman Kernel
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