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。     

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。     

整函数插值序列的稳定性

本文证明了指数π型整函数Bπ，p，1＜p＜∞中某些实插值序列的稳定性，从而证明了存在一个和p有关的正常数δp，使得当sup|uj－j＜δp，u0＝0时，｛Gj（x）｝j∈Z为Bπ，p，1＜p＜∞的一组无条基，其中并且我们还证得是Bπ，p，1＜p＜∞的一组稳定的无条件基．     

ON ENTIRE FUNCTIONS, BLOCH AND NORMAL FUNCTIONS

New criteria for an analytic function to be Bloch and for a meromorphic function to benormal are given. These criteria generalize the recently introduced area integral conditionsinvolving a Green's function.     

THE GROWTH THEOREM FOR BIHOLOMORPHIC MAPPINGS IN SEVERAL COMPLEX VARIABLES

The Growth Theorem for normalized biholomorphic starlike and convex mappings on Reinhardt domains and classical domains are established.     

QUANTITATIVE THEOREM AND SATURATION THEOREM FOR MULTIVARIATE RANDOMFUNCTIONS

1IntroductionSincetheapproximationaboutpositivelinearoperatorscanbenaturallyinterpretedasthecorrespondingtopicsinprobabilitytheoryswecanuseprobabilitymethodtoconstructorsolvetherelatedproblem([1],[2]).Meanwhile,thetechniquesandidealsusedinapproximationtheorycanbeusedtodealwithsomequestionsinprobabilitytheory,especiallytodiscussthelimittheoryandtoestimatetheconvergentrates.Recently,M.WebastudiedthecentrallimittheorybyusingKorovkintheoryinapproximationtheory([1],[2]).Correspondingtoclassofgene…     

求一类多元多峰函数全局极小的区间斜率方法

Based on the interval analysis, an interval slope method is proposed for finding all global minimizers of a several peaks function f on domain X^0包含于R^n, which is given by interval slope discard tests and interval extension of objective function.Numerical results of representative test functions show that this method is practical and effective.     

SHANNON SAMPLING AND ESTIMATION OF BAND-LIMITED FUNCTIONS IN THE SEVERAL COMPLEX VARIABLES SETTING

1IntroductionSystematic studies on sinc function of one complex variable may be traced to the work ofStenger[10].Numerical methods based on the sinc function were subsequently studied in[12].The results arising from the numerical methods were further appl…     

多复变数函数的Schwarz引理

<正> §1.内容的简单介绍当试把Schwarz引理推广到多个复变数论者,曾有H.Cartan,Carathéo-dory,Bergmann,Bochner-Martin,Bureau,Фукс,Ozaki-Kashiwagi-Tsuboi,Sthr.但从这许多的前人之结果中,仍然使人产生一问题,就是Schwarz 引理能否推广与在什么意义下能推广.     

UNIQUENESS OF MEROMORPHIC OR ENTIRE FUNCTIONS AND THEIR DIFFERENTIAL POLYNOMIALS

This article studies the problem of uniqueness of two entire or meromorphic functions whose differential polynomials share a finite set. The results extend and improve on some theorems given in [3].     

NORMAL THEOREMS ON SEVERAL COMPLEX VARIABLES

Suppose that V is a memanll 8phere with unit diameter. It is an one-to-one correspondenceto the close complex plane C. In this paper, they are identified. Let V" be a Riemann sphereof m dimension.Definition 1 Suppose that A = (a1,' t a.,), B = (b1,' l b.) E V". Define sphericaldistallce between two points A, B{lA, Bl. = thet A, B / oc,lA, bol,. = the, B = co,where lAl =.Definition 2 Suppose tl1at f(z) is a homeomorphism from domain D C V to don1ainDl C V. If on the spherical di…     

代数体函数的正规定理

为克服代数函数多值的困难,我们定义了一种新的“距离”,运用它我们证明了一个正规定理,代数体函数族{fj}在区域D上是正规的,当且仅当{fj}是等度连续的。     

UNIQUENESS OF MEROMORPHIC OR ENTIRE FUNCTIONS AND THEIR DIFFERENTIAL POLYNOMIALS

This article studies the problem of uniqueness of two entire or meromorphic functions whose differential polynomials share a finite set. The results extendand improve on some theorems given in [3].     

截断型亚纯映射的唯一性定理涉及到小映射的情形

唯一性定理是多复变值分布中重要的定理之一,本文在已有的研究成果上,运用Thai最新得到的第二基本定理,给出了多复变中截断型亚纯映射新的唯一性定理涉及到小映射情形.     

多個複變數函數論Ⅱ 超球雙曲空間中的一完整正交函數系

<正> §1.引言 在上一篇文章裹,我曾經具體地算出矩陣的雙曲空間中的完整正交函数系,在該文中引用了方陣羣的表示法的理論.在這一篇文章裹,我們將定出超球雙曲空間中的完整正交系.所用的方法和上篇稍有不同,我們除掉用一些正交羣的表示羣以外,還用了不變量論中的結果及若干與球調和(spherical harmonic)     

可列值随机变量序列的一个小偏差定理

本文得到了可列值随机变量序列的用不等式表示的强极限定理,即小偏差定理,包含了［１］的结果．［１］中研究的是相对于齐次Ｍａｒｋｏｖ 链的偏差,而本文允许非齐次的情形．     

多复变整函数涉及全导数的唯一性定理

结合金路提出的多复变上整函数全导数的概念,得到了如下定理:对于n维复欧式空间C~n上两个非常数整函数f和g,以及一个正整数k,如果δ(0,f)+δ(0,g)1,D~kf=1D~kg=1,那么f≡g.这一结论是仪洪勋和杨重骏的定理的推广.     

p-ADIC亚纯函数在截断重级下的一个定理

本文研究p-adic亚纯函数在截断重级下分担两个公共值集的唯一性问题，得到了一个相应的定理．定理的证明主要利用p-adic亚纯函数论中的两个基本定理和一个辅助函数．     

SHARP DISTORTION THEOREMS FOR A CLASS OF BIHOLOMORPHIC MAPPINGS IN SEVERAL COMPLEX VARIABLES

In this paper,we first establish the sharp growth theorem and the distortion theorem of the Frechet derivative for biholomorphic mappings defined on the unit ball of complex Banach spaces and the unit polydisk in Cⁿ with some restricted conditions.We next give the distortion theorem of the Jacobi determinant for biholomorphic mappings defined on the unit ball of Cⁿ with an arbitrary norm and the unit polydisk in Cⁿ under certain restricted assumptions.Finally we ...