含有解析函数与亚纯函数的一些不等式

指出文献 [2 ]和文献 [4]中的错误 ,并且得到含有单位圆盘内接解析函数与亚纯函数的几个不等式 .     

解析函数单叶性的某些充分条件

本文给出了单位圆盘内解析函数单叶性的某些充分条件。     

两类解析函数族的一些性质

研究两类解析函数族的性质，推广了Chichra[4]、Mocanu[5]和Obradovic[6]的一些结果。另外，也指出了S.Owa[8]的一个错误。     

Boundary behavior of the power series of the enlarged Bloch class

We construct the classes of functions analytic in the unit disk, other than lacunary, and possessing the following property: If a function belongs to one of these classes and the sum of the squares of its coefficients is unbounded then there exists a set of positive measure on the circle where the function has no radial limits.     

向量值函数边值问题的典则算子

本文给出复巴拿赫空间的黎曼型边值问题并运用算子的谱表示来研究。首先我们给出跳跃问题的解，然后就连接算子的谱是离散的情形下给出一般边值问题的典则算子。     

Koch曲线所围区域内的一类解析函数边值问题

在经典解析函数边值理论中,当L为复平面上逐段光滑封闭曲线时,在L所围的内部和外部,Cauchy型积分解析;通过对Cauchy主值积分的讨论,可得Cauchy型积分在L上的左、右边值,且边值满足Plemelj公式.基于Koch曲线的构造方法,对一系列Cauchy型积分取极限,并附加上一定的Hlder条件,可得在Koch曲线所围的内部和外部区域内都解析的Cauchy型积分函数,进一步得到与经典解析函数边值问题类似的结果.     

用于解析函数复分析的共轭边界元法

由2个共轭的实调和函数构建1个复解析函数,其复分析在应用数学和力学领域具有重要的作用.提出了一个加权残数方程组,证明了该方程组为2个共轭函数的域内控制方程、边界条件和边界上Cauchy Riemann(柯西-黎曼)条件的近似解,等效为复解析函数的逼近方程.在离散空间中,由该加权残数方程分别推导出2个位势问题的直接边界积分方程和1个表示Cauchy-Riemann条件的有限差分方程,随后解决了弱奇异线性方程组的求解难题,并提出用Cauchy积分公式求内点值的方法,从而建立了一种用于复分析的常单元共轭边界元法.最后,用3个算例证明了所提出方法适用于域内或域外的幂函数、指数函数或对数函数形式的解析函数,而且其误差与2维位势问题是同等量级的.     

关于多值解析函数的教学研究

复变函数论中的多值函数教学是一个难点.钟玉泉先生的教材在这一难点的处理方面是较成功的.他通过例题,介绍多值函数分成单值分支的方法,介绍求函数值的方法,并对这些方法进行了总结,得出的结论是:当给定初值后,只有通过连续变化才能得到其它点的函数值.这一点和传统的代入法求函数值完全不同.然而该教材就在这一总结之后,又用代入法求Arcsin2.我们认为这自我否定了刚刚建立起来的求值方法,扰乱了读者的思想.本文通过对Arcsinz分成单值解析分支的讨论,对求Arcsin2提出了新的教材处理方案,以期和读者商榷.     

Representability of Analytic Functions in Terms of Their Boundary Values

Suppose that is an arbitrary finite complex Borel measure on the interval is its Poisson integral, and are the conjugate harmonics of , and is the nontangential limiting value of the analytic function as . In this paper, we consider the problem of representing the analytic function in terms of its boundary values .     

负系数单叶函数的一个新子族

本文引入了一类具有负系数的单叶函数族C_n(α),并且讨论了这类函数族精确的系数估计,偏差定理及闭包定理,推广了一些已有结果.     

Analytic Discs and Extension of CR Functions

Let M be a manifold of X = C ⁿ , A a small analytic disc attached to M, z ^o a point of A where A is tangent to M, z ¹ another point of A where M extends to a germ of manifold M ₁ with boundary M. We prove that CR functions on M which extend to M ₁ at z ¹ also extend at z ^o to a new manifold M ₂. The directions M ₁ and M ₂ point to, are related by a sort of connection associated to A which is dual to the connection obtained by attaching 'partial analytic lifts' of A to the co-normal bundle to M in X.     

On Brennan's Conjecture for a Special Class of Functions

In this paper, we prove Brennan's conjecture for conformal mappings f of the disk {z : | z| < 1} assuming that the Taylor coefficients of the function log(zf′(z)/f(z)) at zero are nonnegative. We also obtain inequalities for the integral means over the circle |z| = r of the squared modulus of the function zf′(z)/f(z).     

解析函数在本性奇点的一些研究

用正规族理论,研究解析函数在本性奇点附近性质,得到解析函数及其导数在孤立本性奇点附近的一些结果.     

关于随机解析算子函数的正族性质

该文在经典函数的正族理论基础上建立了随机解析算子函数的正族、一致有界和等度连续等概念，并在此意义下，给出了随机解析算子函数族内闭一致有界与等度连续、正族与一致有界的关系，以及随机解析算子函数族为正族的一个充分必要条件。     

关于有限圆盘内解析函数的Hadamard分解定理的结果

In this paper, we investigate the Hadamard factorization theorem of analytic functions in the finite disc DR = {z ∈ C : |z| = r R ∞}, where C is the whole complex plane. Examples are given to show that our results are sharp.     

On Conversion of the L'Hopital Rule for Analytic Functions

We consider the question about the possibility of conversion of the L'Hopital rule for the limits of ratios of analytic functions at a boundary point of the analyticity domain in a Stolz angle.     

Modulus of Continuity of Piecewise Analytic Functions

We obtain conditions under which the modulus of continuity of a piecewise analytic function given on a closed interval of the real axis is an analytic function in a neighborhood of zero.     

双单叶函数某个子类的Faber多项式系数估计

The main objective of this paper is to derive the upper bounds for the coefficients of functions in a subclass of analytic and bi-univalent functions associated with Faber polynomials.The consequences presented here point out and correct the errors of some earlier results.     

由算子定义的一类p叶解析函数性质

通过Hadarnard卷积定义算子I<,n+p-1>,并利用其引进了新的解析函数类H(p,n,δ,A,B),研究了函数f(z)(f(z)∈A<,p>)属于函数类H(p,n,δ,A,B)的充分条件和部分和性质,同时还考虑了类H(p,n,δ,A,B)的卷积性质.     

Boundary derivatives of the phases of inner and outer functions and applications

We prove that boundary derivatives of the phases of inner functions exist and are positive almost everywhere, but those of outer functions, on the other hand, have zero mean on the boundary. The concepts and results have definitive applications to the definitions of instantaneous frequency and mono‐components complying with requirements in physics and contemporary study of analytic signals. Copyright © 2008 John Wiley & Sons, Ltd.