Fredholm Composition Operators on Riemann Surfaces

It is proved that the invertibility of a composition operator on the differential form space for a Riemann surface is equivalent to its Fredholmness. In addition, the Fredholmness of weighted composition operators is discussed.     

紧Riemann面上的复合算子

In the present paper, the characterization of invertible composition oper-ators on compact Riemann surfaces is obtained, which is very different from that in the case of Hardy or Bergman spaces on a disk of the complex plane C.     

Dirichlet空间上的Toeplitz算子

本文研究了Dirichlet空间上的Toeplitz算子,部分的回答了文[1]中的问题,给出了关于Dirichlet空间上Toeplitz算子的一个稠密性定理。     

Toeplitz Operators on Dirichlet Spaces

In this paper we study Toeplitz operators on Dirichlet spaces and describe the boundedness and compactness of Toeplitz operators on Dirichlet spaces. Meanwhile, we give density theorems for Toeplitz operators on Dirichlet spaces Received December 22,1998, Revised March 27, 2000, Accepted June 27, 2000     

Bergman空间上Toeplitz算子的局部化

In this paper we characterize the essential spectra of Toeplitz operators on Bergman spaces by using Douglas‘ localization Theorem and obtain the local decomposition of the essential spectra of Toeplitz operators.     

Bergman空间上Toeplitz算子的凸性

本文讨论了Ｂｅｒｇｍａｎ空间上Ｔｏｅｐｌｉｔｚ算子的凸性，证明了具有调和符号和一类连续函数符号的Ｔｏｅｐｌｉｔｚ算子是凸型算子，并举例说明，存在具有连续函数符号的非凸型Ｔｏｅｐｌｉｔｚ算子。     

Dirichlet空间上Toeplitz算子的紧性

本文给出了 Ｄｉｒｉｃｈｌｅｔ空间上 Ｔｏｅｌｐｉｔｚ算子为紧算子的充要条件,并证明具有 Ｃ１－符号的 Ｔｏｅｐｌｉｔｚ算子为紧算子当且仅当它为零算子,当且仅当符号的边值为零．     

Operators on Sobolev Type Spaces

In this paper, we introduce the work done on Hardy-Sobolev spaces and Fock-Sobolev spaces and their operators and operator algebras, including the study of boundedness, compactness, Fredholm property, index theory, spectrum and essential spectrum, norm and essential norm, Schatten-p classes, and the $C^∗$ algebras generated by them.     

Gromov Hyperbolicity of Riemann Surfaces

We study the hyperbolicity in the Gromov sense of Riemann surfaces. We deduce the hyperbolicity of a surface from the hyperbolicity of its ＂building block components＂. We also prove the equivalence between the hyperbolicity of a Riemann surface and the hyperbolicity of some graph associated with it. These results clarify how the decomposition of a Riemann surface into Y-pieces and funnels affects the hyperbolicity of the surface. The results simplify the topology of the surface and allow us to obtain global results from local information.     

Dirichlet型空间上Toeplitz算子的本性范数

本文研究单位圆盘上Dirichlet型空间非紧Toeplitz算子的本性范数, 它事实上等于到紧Toeplitz算子集的距离. 并且这个距离可由无限多个紧Toeplitz算子来刻画, 这个结果与加权Bergman空间情形的类似.     

多连通区域的Dirichlet空间上的复合算子

对于定义在有界连通区域上的Dirichlet空间,我们着重讨论了其上复合算子的有界性、可逆性、Fredholm性及K-理论性质.     

Hardy空间上的有界复合算子

本文讨论了由解析映射φ：Ｂｎ→Ｂｍ诱导复合算子的有界性；特别地，研究了由保测内映射诱导复合算子的性质．作为推论，得到了Ｗ．Ｒｕｄｉｎ［１０］中一个公开问题的解答．     

齐型空间上的Toeplitz型算子

设X是齐型空间.设T_(j,1)和T_(j,2)是具有非光滑核的奇异积分算子,或者是±II(I是恒等算子).令Toeplitz型算子T_b=■T_(j,1)M_T_(j,2),其中M_bf(x)=b(x)f(x).研究了当b∈BMO(X)时,T_b(f)在加权情况下的有界性,以及当b∈BMO(X)时,与经典Carderon-Zygmund算子相联的T_b(f)在Morrey空间上的有界性.     

单位球上Besov空间的Toeplitz算子

考虑了全纯Besov空间B_p上的Toeplitz算子T_μ~α,这里μ是单位球上的一个复Borel测度.给出了T_μ~α在B_p上有界的一些充要条件.     

对数Bloch空间上积型算子的有界性

让H(D)表示复平面C里的单位圆盘D上的所有解析函数的全体,ψ_1,ψ_2∈H(D),而φ是D到D的解析自映射.本文刻画了对数Bloch空间上积型算子T_(ψ_1,ψ2,φ)的有界性.     

Riemann曲面之间的极值拟共形映射

设Ｓ和Ｒ是两个以单位圆为万有覆盖的Ｒｉｅｍａｎｎ曲面,ｆ：Ｓ→Ｒ为拟共形同胚,类似于ＫＳｔｒｅｂｅｌ的方法。我们引ｉｅｍａｎｎ嗣面Ｓ上的点ｐ０关于模边同伦类「ｆ０」的可变性集合Ｖ「ｆ０」「ｐ０」的概念并且证明可变性集合是Ｒ的一个紧的连通子集。     

加权Bergman空间上的紧算子

本文讨论了加权Ｂｅｒｇｍａｎ空间上的Ｔｏｅｐｌｉｔｚ算子,证明了Ｔｏｐｌｉｔｚ算子的有限乘积的有限和是紧的当且仅当它的Ｂｅｒｅｚｉｎ变换在边界上趋向于零．     

有界连通区域上Dirichlet空间及其算子

本文主要讨论了有界连通区域Dirichlet空间上Toeplitz算子的Fredholm性质,计算了符号在C1中的Toeplitz算子的本性谱和Fredholm指标．     

Generalized Weighted Composition Operators on Weighted Bergman Spaces

The boundedness and compactness of the generalized weighted composition operator on weighted Bergman spaces are discussed.     

Dirac Operators on Hermitian Spin Surfaces

We prove the conformal invariance of the dimension of thekernel of any of the self-adjoint Dirac operators associated to thecanonical Hermitian connections on Hermitian spin surface. In the caseof a surface of nonnegative conformal scalar curvature we estimate thefirst eigenvalue of the self-adjoint Dirac operator associated to theChern connection and list the surfaces on which its kernel isnontrivial.