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 .     

Bazilevic函数相邻两系数模之差的估计

本文研究单叶函数相邻系数模之差的增长问题,设f(z)∈S, 0<λ<1．当f为Bazilevic函数时,得到||Dn+1|-|Dn||的准确的阶的估计．     

解析函数的p叶性条件

本文指出 Ｍ．Ｊａｈａｎｇｉｒｉ的评论［Ｍａｔｈｅｍａｔｉｃａｌ Ｒｅｖｉｅｗｓ　９８ｅ：３００２０］错误，并且导出解析函数ｐ叶星形性与ｐ叶凸性的某些充分条件．     

解析函数与Lipschitz条件

研究了解析函数与Lipschitz条件,得到了如下两个结果:(i)设D是一平面区域,f(z)在D中解析,00,对任意z∈D有|f′(z)|≤md(z,D)k-1,则f∈Lipk(D)且‖f‖k≤cmk,其中c=c(D)是仅与D有关的常数.     

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.     

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.     

L2-Estimates and Existence Theorems for Generalized Analytic Functions in Several Variables

We consider the generalized Cauchy–Riemann system with nonlinear terms in an arbitrary domain of the complex space. Under some natural conditions on the coefficients and compatibility conditions, we prove solvability of this system in the space of locally square integrable functions.     

Some Remarks on Equivalence of Moduli of Smoothness

The present paper investigates polynomials for which the inverse inequality for moduli of smoothness holds. The technique for approach is different from the previous works for splines and is elegantly organized.     

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.     

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.     

关于解析函数的一个易想象的不等式及其应用

本文关于解析函数给出了一个可作几何理解的不等式,由此易得出一个有关解析函数零点的命题,而代数学基本定理成为它的直接推论．     

凸函数的β可微性和光滑模

本文引入一类特殊的实值函数(模),并由此对Banach空间上凸函数的Fréchet可微性,更一般地,β-可微性进行了特征刻画.     

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。     

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。     

Infinitesimal adjunction and polar curves

The polar curves of foliations having a curve C of separatrices generalize the classical polar curves associated to hamiltonian foliations of C. As in the classical theory, the equisingularity type ℘() of a generic polar curve depends on the analytical type of , and hence of C. In this paper we find the equisingularity types ε(C) of C, that we call kind singularities, such that ℘() is completely determined by ε(C) for Zariski-general foliations . Our proofs are mainly based on the adjunction properties of the polar curves. The foliation-like framework is necessary, otherwise we do not get the right concept of general foliation in Zariski sense and, as we show by examples, the hamiltonian case can be out of the set of general foliations. The author was partially supported by the research projects MTM2007-66262 (Ministerio de Educación y Ciencia), MTM2006-15338-C02-02 (Ministerio de Educación y Ciencia),VA059A07 (Junta de Castilla y León) and PGIDITI06PXIB377128PR (Xunta de Galicia).     

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。     

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.     

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.     

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.