Montel正规定则的推广(英文)

用简单的方法证明了全纯函数族的一个正规定则,推广了Montel正规定则.设F为区域D上的一个全纯函数族,其零点是重级的,a为有限复数.如果f,g∈F,有(f-1)f′与(g-1)g′分担a,则F正规.     

多复变Pang-Zalcman引理及应用

单复变中的Pang-Zalcman引理是研究亚纯函数正规族问题的重要工具.本文将该引理推广至多复变全纯函数的情形.作为应用建立了多复变全纯函数族的正规定则，改进和推广了相关结果.     

关于多元复函数的正规族

研究函数族的正规性定则是复变函数论中的一个重要且有意义的工作,本文通过引进多元Ｋ－拟亚纯函数（或Ｋ－全纯函数）的定义,得到了多元Ｋ－拟亚纯函数（或Ｋ－全纯函数）族的一个正规定则,据此讨论了多元纯函数（族的若干正规性定则。     

涉及复代数超曲面的全纯映射正规族（英文）

本文研究了涉及固定超曲面的全纯映照的正规性问题.利用Aladro和Krantz对全纯映射族正规性的刻画和Shirosahi建立的一系列涉及一些特殊复代数超曲面的Picard型定理,得到了全纯映射族的一些正规定则.     

涉及复代数超曲面的全纯映射正规族

本文研究了涉及固定超曲面的全纯映照的正规性问题。利用Aladro 和Krantz对全纯映射族正规性的刻画和Shirosahi建立的一系列涉及一些特殊复代数超曲面的Picard 型定理,得到了全纯映射族的一些正规定则。     

多复变函数的Picard定理

本文给出了多复变函数的Ｋ－拟亚纯函数的定义,并且得到了一个关于多复变函数的Ｋ－拟亚纯函数的正规定则,从这个正规定则,我们证明了多复变函数的全纯函数Ｐｉｃａｒｄ定理。     

亚纯函数族结合导数涉及重值时的正规性

<正> §1.引言 杨乐、张广厚对全纯函数族结合导数涉及重值时的正规性进行了研究,他们得到了如下结果. 定理A.设∑为平面区域Ω上的全纯函数族.若f∈∑有:f(z)的零点的重级均≥m,f~((k))(z)-1的零点的重级均≥n,且k+1/m+1/n<1,则∑在Ω内正规.     

涉及分担数组的唯一性和正规性

本研究涉及分担一个数组的整函数的唯一性,并得到相应的全纯函数的正规定则。     

一类全纯函数的正规性

研究了具有一定性质的全纯函数.设F是平面上区域D内的全纯函数族.如果对于任意的f∈F,都有f(z)=0 f'(z)=z j|f″(z)|≤c,其中c为常数且f(0)≠0,则F正规.     

关于全纯函数的正规定则

研究涉及微分多项式与公共值的全纯函数族的正规性问题.设F为区域D内的全纯函数族,n 1为任一正整数,b为有限常数,如果对F中任意两个函数f与g,fn(f-1)f′与gn(g-1)g′在D内都以b为公共值,则F在D内正规.此结果对亚纯函数不成立.     

On Weighted Spaces of Harmonic and Holomorphic Functions

Weighed spaces of harmonic and holomorphic functions on theunit disc are studied. We show that for all radial weights whichare not decreasing too fast the space of harmonic functionsis isomorphic to c₀. For the weights that we consider we completelycharacterize those spaces of holomorphic functions which areisomorphic to c₀. Moreover, we determine when the Riesz projection,mapping the weighted space of harmonic functions onto the correspondingspace of holomorphic functions, is bounded.     

The Cauchy‐Kowalewski product for bicomplex holomorphic functions

In this paper we study the Cauchy‐Kowalewski extension of real analytic functions satisfying a system of differential equations connected to bicomplex analysis, and we use this extension to study the product in the space of bicomplex holomorphic functions. We also show how these ideas can be used to define a Fourier transform for bicomplex holomorphic functions.     

Some new results on domains in complex space with non-compact automorphism group

We provide a new proof of the Wong-Rosay theorem, using the structure of the ring of holomorphic functions. As a byproduct, we provide an analogous theorem for classical bounded symmetric domains. The second main result of this article concerns a new existence theorem for holomorphic peaking functions at a hyperbolic orbit accumulation boundary point. Finally, we give a proof of a version of the Greene-Krantz conjecture using holomorphic vector fields and a strengthened Hopf lemma.     

WEIGHTED HOLOMORPHIC BESOV SPACES AND THEIR BOUNDARY VALUES

We study weighted holomorphic Besov spaces and their boundary values. Under certain restrictions on the weighted function and parameters, we establish the equivalent norms for holomorphic functions in terms of their boundary functions. Some results about embedding and interpolation are also included.     

Representation of holomorphic functions on coverings of pseudoconvex domains in Stein manifolds via integral formulas on these domains

The classical integral representation formulas for holomorphic functions defined on pseudoconvex domains in Stein manifolds play an important role in the constructive theory of functions of several complex variables. In this paper, we will show how to construct similar formulas for certain classes of holomorphic functions defined on coverings of such domains.     

高维复域中非线性全特征方程的全纯解

本文在全纯函数类中研究了一类定义在高维复域中的非线性奇异偏微分方程,在一定条件下,证明了其局部全纯解的存在性与唯一性．     

The summarized equation for functions which are holomorphic in the exterior of a triangle

We consider the six-element summarized equation in the class of functions which are holomorphic in the exterior of a regular triangle and vanishing at infinity. We apply the method of integral equations and the theory of elliptic functions. Using the obtained results, we construct biorthogonal systems of holomorphic functions and study the problem of moments for integer functions of a finite degree.     

复Banach空间中C-R方程的全纯解

二重复数是复数的一种推广，在其上的全纯映照族对应于Ｃ２上满足复Ｃａｕｃｈｙ－Ｒｉｅｍａｎｎ方程的全纯映照族．可以证明，这样的映照族本质上是由二个单复变数的全纯函数的直乘积所组成的族．本文证明：即使在Ｂａｎａｃｈ空间中，Ｃａｕｃｈｙ－Ｒｉｅｍａｎｎ方程的全纯解，具有同样的性质．     

The Cauchy Transform of Continuous Linear Functionals and Projections on the Weighted Spaces of Analytic Functions

Under some general assumptions on weight, we give a complete characterization of the Cauchy transform of continuous linear functionals on the weighted spaces of holomorphic functions in a ball. We construct an integral projection that sends the weighted spaces of measurable and n-harmonic functions in the ball onto the corresponding spaces of holomorphic functions.     

Hypercyclic convolution operators on Fréchet spaces of analytic functions

A result of Godefroy and Shapiro states that the convolution operators on the space of entire functions on Cn, which are not multiples of identity, are hypercyclic. Analogues of this result have appeared for some spaces of holomorphic functions on a Banach space. In this work, we define the space holomorphic functions associated to a sequence of spaces of polynomials and determine conditions on this sequence that assure hypercyclicity of convolution operators. Some known results come out as particular cases of this setting. We also consider holomorphic functions associated to minimal ideals of polynomials and to polynomials of the Schatten-von Neumann class.