上半平面上Bergman投影的有界性

利用再生核定义了Bergman投影算子,给出了Bergman投影算子有界性的充分条件.     

Bergman空间上的复合算子的范数

本文研究了Bergman空间上的复合算子的范数与再生核的关系,证明了紧复合算子C的范数‖C‖=sup{‖C*kw‖:w∈D}的充要条件是(0)=0或是仿射映射,即(z)=sz+t,s,t是满足|s|+|t|<1的常数,其中kw为Bergman空间的规范再生核, C*是C的共轭算子.     

关于L~2(D)的解析再生核闭子空间(英文)

如果Ｄ为复平面上的单位圆盘,本文证明了从本质上说,Ｌ~２（Ｄ）的闭的解析再生核Ｈｉｌｂｅｒｔ空间仅仅是Ｂｅｒｇｍａｎ空间．     

Bergman度量的完备性

本文证明了两个定理：（１）设ＤＣｎ是一个完备的圆型域,若且对任意．则Ｄ对ρＤ而言是完备的．（２）令Ｄ是Ｃｎ中的有界域,若其 Ｂｅｒｇｍａｎ核函数ＫＤ（ｚ,）满足下列条件：（ｉ）ＫＤ（ｚ,）在 Ｄ ｘ（Ｄ∪ Ｄ）连续;（ｉｉ）对任何 Ｐ ∈Ｄ,有ｌｉｍ ＫＤ（ｚ,ｚ）＝ ＋∞．则 Ｄ对 ρＤ而言是完备的．作为其应用,还证明了Ｃａｒｔａｎ－Ｈａｒｔｏｇｓ域在其 Ｂｅｒｇｍａｎ度量下是完备的．     

加权调和Bergman核及其诱导的度量矩阵

在Rn中的有界域上建立加权调和Bergman核,并得出单位球的加权调和Bergman核的表达式;利用加权调和Bergman核在Rn的有界域上构造度量矩阵;得到关于调和映射的Jacobi矩阵与度量矩阵之间的一个不等式.     

再生核空间中求解带有积分边界条件的半线性热传导方程

该文给出了一个新的方法来求解带有积分边界条件的半线性热传导方程.方程的精确解以级数的形式在再生核空间中给出.证明了精确解的n项逼近是收敛于精确解的.同时给出了一些算例说明了这个方法的有效性.     

Bergman度量的完备性

本文证明了两个定理(1)设DcCn是一个完备的圆型域,若λ(D∪D)cD(0≤|λ|＜1),且对任意p∈D,有     

半平面函数空间上复合算子的差分

本文刻画半平面Korenblum空间上复合算子差分的有界性、紧性和序有界性,并探究复合算子差分的相应性质在半平面Bergman空间与Korenblum空间之间的差异性.     

Reproducing kernel method of solving singular integral equation with cosecant kernel

In the paper, a reproducing kernel method of solving singular integral equations (SIE) with cosecant kernel is proposed. For solving SIE, difficulties lie in its singular term. In order to remove singular term of SIE, an equivalent transformation is made. Compared with known investigations, its advantages are that the representation of exact solution is obtained in a reproducing kernel Hilbert space and accuracy in numerical computation is higher. On the other hand, the representation of reproducing kernel becomes simple by improving the definition of traditional inner product and requirements for image space of operators are weakened comparing with traditional reproducing kernel method. The final numerical experiments illustrate the method is efficient.     

Weighted reproducing kernels and Toeplitz operators on harmonic Bergman spaces on the real ball

For the standard weighted Bergman spaces on the complex unit ball, the Berezin transform of a bounded continuous function tends to this function pointwise as the weight parameter tends to infinity. We show that this remains valid also in the context of harmonic Bergman spaces on the real unit ball of any dimension. This generalizes the recent result of C. Liu for the unit disc, as well as the original assertion concerning the holomorphic case. Along the way, we also obtain a formula for the corresponding weighted harmonic Bergman kernels.

     

Bergman kernel and metric on non-smooth pseudoconvex domains

A stability theorem of the Bergman kernel and completeness of the Bergman metric have been proved on a type of non-smooth pseudoconvex domains defined in the following way:D = {z∈U|r(z)} <whereU is a neighbourhood of andr is a continuous plurisubharmonic function onU. A continuity principle of the Bergman Kernel for pseudoconvex domains with Lipschitz boundary is also given, which answers a problem of Boas.     

Behavior of the Bergman kernel and metric near convex boundary points

The boundary behavior of the Bergman metric near a convex boundary point of a pseudoconvex domain is studied. It turns out that the Bergman metric at points in the direction of a fixed vector tends to infinity, when is approaching , if and only if the boundary of does not contain any analytic disc through in the direction of .

     

On the Bergman metric of pseudoconvex domains in a complex projective space

We prove a localization principle of the Bergman kernel form and metric for pseudoconvex domains in the complex projective space. An estimate of the Bergman distance is also given.