where , ; and let be the Bergman kernel function of . Then there exist two positive constants and and a function such that
holds for every . Here
and is the defining function for . The constants and depend only on and , not on .
The Bergman kernel function for Hua Construction of the third type is given in an explicit formula.
相似文献
相似文献
10.
So-Chin Chen 《Proceedings of the American Mathematical Society》1996,124(6):1807-1810
In this paper we prove the following main result. Let be a smoothly bounded pseudoconvex domain in with . Suppose that there exists a complex variety sitting in the boundary ; then we have
In particular, the Bergman kernel function associated with the Diederich-Fornaess worm domain is not smooth up to the boundary in joint variables off the diagonal of the boundary. 11.
Stefan Jakobsson 《Arkiv f?r Matematik》2002,40(1):89-104
The harmonic Bergman kernelQ Ω for a simply, connected planar domain Ω can be expanded in terms of powers of the Friedrichs operatorF Ω ║F Ω║<1 in operator norm. Suppose that Ω is the image of a univalent analytic function ø in the unit disk with ø' (z)=1+ψ (z) where ψ(0)=0. We show that if the function ψ belongs to a spaceD s (D),s>0, of Dirichlet type, then provided that ║ψ║∞<1 the series forQ Ω also converges pointwise in $\bar \Omega \times \bar \Omega \backslash \Delta (\partial \Omega )$ , and the rate of convergence can be estimated. The proof uses the eigenfunctions of the Friedrichs operator as well as a formula due to Lenard on projections in Hilbert spaces. As an application, we show that for everys>0 there exists a constantC s >0 such that if ║ψ║ D s(D)≤C s , then the biharmonic Green function for Ω=ø (D) is positive. 相似文献
12.
13.
Bergman kernel function on Hua Construction of the second type 总被引:7,自引:0,他引:7
ZHANG Liyou Department of Mathematics Capital Normal University Beijing China 《中国科学A辑(英文版)》2005,48(Z1)
In this paper, we give an explicit formula of the Bergman kernel function on Hua Construction of the second type when the parameters 1/p1,…,1/(pr-1) are positive integers and 1/pr is an arbitrary positive real number. 相似文献
14.
Hugo M. Campos Vladislav V. Kravchenko 《Mathematical Methods in the Applied Sciences》2020,43(16):9448-9454
The paper extends some well-known results for analytic functions onto solutions of the Vekua equation regarding the existence and construction of the Bergman kernel and of the corresponding Bergman projection operator. 相似文献
15.
In this paper, we give an explicit formula of the Bergman kernel function on Hua Construction of the second type when the parameters 1/p1, ..., 1/pr−1 are positive integers and 1/pr is an arbitrary positive real number. 相似文献16.
We define the Cartan–Hartogs domain, which is the Hartogs type domain constructed over the product of bounded Hermitian symmetric domains and compute the explicit form of the Bergman kernel for the Cartan–Hartogs domain using the virtual Bergman kernel. As the main contribution of this paper, we show that the main part of the explicit form of the Bergman kernel is a polynomial whose coefficients are combinations of Stirling numbers of the second kind. Using this observation, as an application, we give an algorithmic procedure to determine the condition that their Bergman kernel functions have zeros. 相似文献
17.
18.
The purpose of this paper is to study singularities of the Bergman kernel at the boundary for pseudoconvex domains of finite type from the viewpoint of the theory of singularities. Under some assumptions on a domain in
n+1
, the Bergman kernel B(z) of takes the form near a boundary point p:
where (w,) is some polar coordinates on a nontangential cone with apex at p and means the distance from the boundary. Here admits some asymptotic expansion with respect to the variables 1/
m
and log(1/) as 0 on . The values of d
F
>0, m
F
+ and m are determined by geometrical properties of the Newton polyhedron of defining functions of domains and the limit of as 0 on is a positive constant depending only on the Newton principal part of the defining function. Analogous results are obtained in the case of the Szegö kernel.
Mathematics Subject Classification (2000):32A25, 32A36, 32T25, 14M25. 相似文献
19.
We get the Bergman kernel functions in explicit formulas on four types of Hua domain.There are two key steps: First, we give the holomorphic automorphism groups of four types of Hua domain; second, we introduce the concept of semi-Reinhardt domain and give their complete orthonormal systems. Based on these two aspects we obtain the Bergman kernel function in explicit formulas on Hua domains. 相似文献
20.
The Bergman kernel and biholomorphic mappings of pseudoconvex domains 总被引:10,自引:0,他引:10
Charles Fefferman 《Inventiones Mathematicae》1974,26(1):1-65
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