Families of Normal Maps in Several Complex Variables and Hyperbolicity of Complex Spaces

In this article, generalizations of the theorem of Zalcmal to complex spaces are given. Moreover, a generalization of Five-Point Theorem of Lappan to complex projective algebraicmanifolds also is shown.     

On Spirallike Mappings in Several Complex Variables

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＩｎ１９３３,Ｈ．ｃａｒｔａｎｐｏｉｎｔｅｄｏｕｔｔｈａｔｔｈｅｒｅｄｏｅｓｎｏｔｅｘｉｓｔｔｈｅｃｏｒｒｅｓｐｏｎｄｉｎｇＢｉｅｂｅｒｂａｃｈｃｏｎ－ｊｅｃｔｕｒｅｆｏｒｂｉｈｏｌｏｍｏｒｐｈｉｃｍａｐｐｉｎｇｓｉｎｓｅｖｅｒａｌｃｏｍｐｌｅｘｖａｒｉａｂｌｅｓ．Ｈｅａｌｓｏｐｏｉｎｔｅｄｏｕｔｔｈｅｃｏｒｒｅ－ｓｐｏｎｄｉｎｇｇｒｏｗｔｈａｎｄｃｏｖｅｒｉｎｇｔｈｅｏｒｅｍｓｆａｉｌｉｎｔｈｅｃａｓｅｏｆｓｅｖｅｒａｌｃｏｍｐｌｅｘｖａｒｉａｂｌｅｓ．Ｔｈｅｎ…     

关于多复变数微分从属的一个注记

我们知道，微分从属是非常有用的，在单叶函数，微分方程和微分不等式等方面都有一定的作用．在这个方面S S Miller，P T Maeanu和龚升等人都作了大量的工作(见[1-3])．本人在这个也做了一些探索，丰富了这个领域的内容(见[4-6])．本文将给出一个很有意思的结果．它将为研究多复变的微分不等式起到一定的作用．为了方便先给出一些记号如下：     

多复变数微分从属的最优控制

讨论了多复变函数中的微分从属的最优控制的问题，取得了一些结果，得到了一些应用．它是单复变函数论中的相应结果[1，2]的推广．     

On the Essential Commutant of Toeplitz Operators in Several Complex Variables

Using the joint local mean oscillation, Jingbo Xia [13] showed that the essential commutant of , where is the subalgebra of L ^∞ generated by all functions which are bounded and have at most one discontinuity, is (QC). Even though Xia’s method cannot be used, we are able to generalize his result to Toeplitz operators in higher dimensions with a different approach. This result is stronger than the well-known result stating that the essential commutant of the full Toeplitz algebra is (QC).      

多复变数的双全纯映照

本文对复变数几何函数论的结果向多复变函数的推广进行了系统的研究，是作者及其合作者们在此项研究工作上的一些成果的综合报导。此文集中讨论了有界对称域及Ｒｅｉｎｈａｒｄｔ域的情形，讨论了全纯映照为星形、凸及双全纯的种种条件，建立了一些双全纯映照族的偏差定理，增长定理及掩盖定理，定义了高维空间上的Ｓｃｈｗａｒｔｚ导数。对有界对称域上的全纯凸函数的Ｂｌｏｃｈ常数进行了估计，处理这些问题的主要工具之一为李代数     

多复变数的抛物星形映射

本文给出了抛物星形映射,ρ次的抛物星形映射,抛物形β型螺形映射和ρ次的抛物形β型螺形映射的定义.证明了推广的Rope-Suffridge算子保持这些映射的几何性质不变.     

非交换非结合的多复变

多复变在非交换非结合领域的推广近年来取得了迅猛的发展.本文简单介绍这方面的最新进展,其中包括切片Clifford分析、离散Clifford分析、Hermitian Clifford分析、Dunkl Clifford分析、四元数分析、八元数分析,离散复分析在统计物理中Ising模型的应用,以及与切片Clifford分析相关的S-谱理论在量子物理的应用.     

On Meromorphically Normal Families of Meromorphic Mappings of Several Complex Variables into P(C)

We shall prove some meromorphic normality criteria for families of meromorphic mappings of several complex variables into P^N(C), the complex N-dimensional projective space, related to Nochka's Picard type theorems. Some related results (e.g., extension theorems, improved normality criteria, and quasi-normality criteria) will be obtained also. The technique in this paper mainly depends on Stoll's normality criteria for families of non-negative divisors on a domain of Cⁿ.     

Commuting of Toeplitz Operators in Several Complex Variables

1 IntroductionLet be the unit ball Bn or the polydisk Dn in Cn, and dA denote the Lebesgue measure on , normalized so that the measure of equals 1. L2/a() is The Bergman space. For z, the Bergman reproducing kernel is a function Kz L2/a). The normalized Bergman reproducing kernel k is the function Kz Kz2. Here, as elsewhere in this paper, the norm 2 and the inner product are taken in the space L2(,dA).Let P denote the orthogonal projection of L2(, dA) onto L2/a(). For a function f L …     

Bloch Functions in Several Complex Variables, I

Bloch functions on the unit disk are those analytic functionsf for which the quantity |f'(z)|(1 – |z|²) is bounded(for z in the disk). In this paper, Bloch functions on boundedhomogeneous domains in complex m-space are studied. The mainresult shows that many of the equivalent definitions of Blochfunctions on the unit disk are also equivalent in the generalsetting. Current Address: 39 Trinity College, Dublin 2, Ireland.     

Finite-Rank Products of Toeplitz Operators in Several Complex Variables

For any α > −1, let A²_α be the weighted Bergman space on the unit ball corresponding to the weight (1 – |z|²)^α. We show that if all except possibly one of the Toeplitz operators are diagonal with respect to the standard orthonormal basis of A²_α and has finite rank, then one of the functions must be the zero function.      

Existence of Generalized Cauchy-Riemann Side-Systems in Several Complex Variables

In the present paper we have deduced the necessary and sufficient conditions on which an initial value problem $\fraca {\partial w}{\partial z_j} = a_j(z,\overline {z})\overline {w}+b_j(z,\overline {z})w+c_j(z,\overline {z}), \, j = 1,\ldots , n,\, w(z_0,\overline {z_0}) = w_0$ is locally solvable in the class of generalized analytic functions of several complex variables, which are functions fulfilling generalized Cauchy-Riemann System, $\fraca {\partial w}{\partial \overline {z_k}} = \overline {\alpha _k(z,\overline {z})}\, \overline {w}+ \overline {\beta _k(z,\overline {z})}w+ \overline {\gamma _k(z,\overline {z})},\, k = 1,\ldots , n$ .     

多复变数星形映照的两类子族

本文首先讨论有界星形圆型域上星形映照的一个子族---次星形映照,着重研究其几何性质,包括增长定理与掩盖定理.然后,在有界凸圆型域上讨论星形映照的另一类子族---α次的γ-凸映照.讨论它与星形映照,β次星形映照以及凸映照的关系.     

Composition Operators on the Bloch Space of Several Complex Variables

Abstract In this paper, we study the boundedness and compactness of composition operator C _φ on the Bloch space β(Ω), Ω being a bounded homogeneous domain. For Ω = B _n, we give the necessary and sufficient conditions for a composition operator C _φ to be compact on β(B _n) or β ₀(B _n). Supported by the National Natural Science Foundation and the National Education Committee Doctoral Foundation     

多元拟亚纯映射的正规族

文章应用覆盖曲面的几何方法讨论了多元拟亚纯映射的正规定理。