Pseudoconvexity and Analytic Discs

The purpose of this paper is to investigate the geometry of pseudoconvex hypersurfaces and their interrelation with analytic discs. The method of analytic discs is a very powerful tool in the study of pseudoconvexity. One way to use this tool is via the so-called type function introduced by Dwilewicz and Hill for arbitrary Cauchy–Riemann manifolds. In the hypersurface case, and moreover, under the assumption of pseudoconvexity, it has additional properties which are given in this paper. As an application, boundary estimates of plurisubharmonic functions are given.     

Analytic Representation of CR Functions on Hypersurfaces with Singularities

We prove a theorem on analytic representation of integrable CR functions on hypersurfaces with singular points. Moreover, the behaviour of representing analytic functions near singular points is investigated. We are aimed at explaining the new effect caused by the presence of a singularity rather than at treating the problem in full generality.     

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.     

Approximation of Singular Discs for CR Extension

We introduce a class of singular discs, modelled on the one introduced by Zaitsev, Zampieri and the author. We show that they gain regularity from reparametrization and from taking powers. We set up a Bishop equation to attach these discs to a CR manifold with smooth dependence on parameters. By these tools we get extension of CR functions from wedges endowed with the sector property.     

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.     

Analytic sets and the boundary regularity of CR mappings

It is shown that if a continuous CR mapping between smooth real analytic hypersurfaces of finite type in extends as an analytic set, then it extends as a holomorphic mapping.

     

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．     

Extension and approximation of CR functions on tube manifolds

A complete generalization of the classical Bochner theorem for infinite tubes is given.

     

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.     

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。     

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.     

Analytic Extension of Smooth Functions

Let F be a closed proper subset of ?ⁿ and let ?* be a class of ultradifferentiable functions. We give a new proof for the following result of Schmets and Valdivia on analytic modification of smooth functions: for every function ? ∈ ?* (?ⁿ) there is ${\widetilde f} \in {\cal E}_{*}(\rm R ^{n})$ which is real analytic on ?ⁿF and such that ?^a ? ¦ _F = ?^a ? ¦ _F for any a ∈ ?₀ ⁿ. For bounded ultradifferentiable functions ? we can obtain ${\widetilde f}$ by means of a continuous linear operator.     

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．     

Analytic Extension of Functions from Analytic Hilbert Spaces

Let M be an invariant subspace of Hv2. It is shown that for each f∈M⊥, f can be analytically extended across (?)Bd\σ(Sz1,…, Szd).     

可变幅角复系数的解析函数族

研究了在单位开圆盘内单叶解析且规范化的复系数函数族gφ1,φ2,φ3,φ4（m1,m2,m3,m4;λ）的一些性质,给出了其子族gφ1,φ2,φ3,φ4（m1,m2,m3,m4;λ）在内闭一致收敛拓扑下的极值点和支撑点,并讨论解决了gφ1,φ2,φ3,φ4（m1,m2,m3,m4;λ）与凸函数相关的一些半径问题,推广了近来的一些研究结果．     

The Starlikeness of Analytic Functions of Koebe Type with Complex Order

For α 0, λ 0 and β,η∈R, we consider the M(α,λ)_b of normalized analyticα—λ convex functions defined in the open unit disc U. In this paper we investigate the class M(α, λ,β,η)_b,with f_b := z/(1-z~n)~b being Koebe type. By making use of Jack's Lemma as well as several differential and other inequalities, the authors derive sufficient conditions for starlikeness of the class M(α, λ, β, η)_b of n-fold symmetric analytic functions of Koebe type. Relevant connections of the results presented here with those given in earlier works are also indicated.     

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。     

Existence of Moduli for Bi-Lipschitz Equivalence of Analytic Functions

We show that the bi-Lipschitz equivalence of analytic function germs (², 0)(, 0) admits continuous moduli. More precisely, we propose an invariant of the bi-Lipschitz equivalence of such germs that varies continuously in many analytic families f _t : (², 0)(, 0). For a single germ f the invariant of f is given in terms of the leading coefficients of the asymptotic expansions of f along the branches of generic polar curve of f.