Banach空间中凸映照的增长定理

本文利用凸映照的几何特征证明了一般复Banach空间中单位球上正规化双全纯凸映照的增长定理，即||f(x)||≤||x||/(1-||x||),A↓x∈B，对复内积空间，上述估计是最佳的。     

一类多复变全纯映照子族的增长和偏差定理

在一般复Banach空间X中的单位球B上引入一类全纯映照族M_g.考虑B上满足条件(Df(x))~(-1)f(x)∈M_g的正规化局部双全纯映照f(x)(其中x=0是f(x)-x的k+1阶零点)并得到其增长定理.作为应用,也得到了C~n中单位多圆柱D~n上映照f关于Jacobi矩阵Jf(z)的偏差定理,该结果统一和推广了星形映照许多子族的相应结论.     

C~n中Lie球R_(Ⅳ)(n)上的偏差定理

本文引入了Lie球双曲空间上映照族Hm(RIV(n)),满足m阶Jacobi行列式为零的全纯映照子族.而且当m趋于无穷时,该映照族就是RIV(n)上的局部双全纯映照族.作者用分析的方法给出了Hm(RIV(n))上的偏差定理.当m=1和m→+∞时,结果分别都回到了Gong关于Lie球RIV(n)上的偏差定理;当n=1,其结果又回到了Liu和Minda在单位圆盘上的偏差定理.本文的方法也不同于以前.作为偏差定理的一个应用,给出了不同映照族Hm(RIV(n))上的Bloch常数估计.     

ε星形映照族(Ⅱ)

在文[1]中定义了e星形映照族,给出了其在复Banach空间及Cn中的域上的判别准则,讨论了Roper-Suffridge算子.本文将进一步讨论Roper-Suffridge算子,并给出单位圆上ε星形映照族的增长定理的上界估计.     

C^n中Lie球RIV（n）上的偏差定理 献给钟同德教授八十华诞

本文引入了Lie球双曲空间上映照族Hm（RIV（n））,满足m阶Jacobi行列式为零的全纯映照子族．而且当m趋于无穷时,该映照族就是RIV（n）上的局部双全纯映照族．作者用分析的方法给出了Hm（RIV（n））上的偏差定理．当m=1和m→＋∞时,结果分别都回到了Gong关于Lie球RIV（n）上的偏差定理;当n=1,其结果又回到了Liu和Minda在单位圆盘上的偏差定理．本文的方法也不同于以前．作为偏差定理的一个应用,给出了不同映照族Hm（RIV（n））上的Bloch常数估计．     

有界星形圆型域上α次殆星映照的增长定理

本文研究了有界星形圆型域上α次生映照,给出其增长定理,所讨论的域是最广泛的,若域不是星形的,则其上不存在星形映照。     

两类螺形映照扩充子族的偏差上界估计

偏差估计一直是多复变函数论的研究热点之一.但目前螺形映照扩充子族的偏差估计的研究成果还较少.针对这一问题,研究了复向量空间C_n中开单位球B_n,复Banach空间中单位球B和域Ω_(p_1,…,p_n)上一类α次β型,α次强β型螺形映照的偏差估计问题.利用不等式、矩阵及两类映照的增长定理等方法,获得了上述域上的两种映照的偏差上界估计,所得结果推广了一些已知的结论.     

一类近于凸映照子族精确的偏差定理

首先建立了C~n中单位多圆柱上一类近于凸映照子族精确的偏差定理,同时在复Banach空间单位球上也建立了该类映照精确的偏差定理的下界估计.其次在复Banach空间单位球上建立了准星形映照精确的偏差定理.所得结果将单复变中近于凸函数和星形函数的偏差定理推广至高维情形,并且对龚升提出的一个公开问题给出肯定的回答.     

Banach空间中星形映照的增长定理与1/4定理

本文给出了一般 Banach空间中单位球上正规化双全纯星形映照的增长定理与 1/4-掩盖定理。特别给出了C~n中单位超球、B~p域、多圆柱和四类典型域上的相应定理。而且在所有情况下估计均为精确的。     

ε星形映照族(Ⅱ)

在文[1]中定义了ε星形映照族,给出了其在复Banach空间及C~n中的域上的判别准则,讨论了Roper-Suffridge算子,本文将进一步讨论Roper-Suffridge算子,并给出单位圆上ε星形映照族的增长定理的上界估计。     

α次β型螺形映照的增长与掩盖定理

In this paper,we consider growth and covering theorem for f(x),where f(x) is spiallike mapping of typeβwith orderαdefined on unit ball B of complex Banach space, and x=0 is zero of order k+1 for f(x)-x.We also dicate that the estimation is precise whenβ=0 and still give growth upper bound and distortion upper hound for subordinate mapping.This result include some results known.     

On Growth and Covering Theorem for Spiallike Mapping of Type β with Order α

In this paper,we consider growth and covering theorem for f(x),where f(x)is spiallike mapping of type β with order α defined on unit ball B of complex Banach space,and x=0 is zero of order k+1 for f(x)-x.We also dicate that the estimation is precise when β=0 and still give growth upper bound and distortion upper bound for subordinate mapping.This result include some results known.     

广义变分不等式与极大极小定理

本文讨论映Hausdorff拓扑线性空间到Riesz空间[6]的算子变分问题.给出半序空间上变分不等式的绝对形式和相对形式.     

Statistical properties for nonhyperbolic maps with finite range structure

We establish the central limit theorem and non-central limit theorems for maps admitting indifferent periodic points (the so-called intermittent maps). We also give a large class of Darling-Kac sets for intermittent maps admitting infinite invariant measures. The essential issue for the central limit theorem is to clarify the speed of -convergence of iterated Perron-Frobenius operators for multi-dimensional maps which satisfy Renyi's condition but fail to satisfy the uniformly expanding property. Multi-dimensional intermittent maps typically admit such derived systems. There are examples in section 4 to which previous results on the central limit theorem are not applicable, but our extended central limit theorem does apply.

     

Linear Maps Preserving Invertibility or Related Spectral Properties

We survey some recent results on linear maps on operator algebras that preserve invertibility. We also consider related problems such as the problem of the characterization of linear maps preserving spectrum, various parts of spectrum, spectral radius, quasinilpotents, etc. We present some results on elementary operators and additive operators preserving invertibility or related properties. In particular, we give a negative answer to a problem posed by Gao and Hou on characterizing spectrumpreserving elementary operators. Several open problems are also mentioned.     

Multiplicity of solutions for semilinear variational inequalities via linking and ∇-theorems

We prove the existence of three distinct nontrivial solutions for a class of semilinear elliptic variational inequalities involving a superlinear nonlinearity. The approach is variational and is based on linking and ∇-theorems. Some nonstandard adaptations are required to overcome the lack of the Palais-Smale condition.     

Periodic structure of transversal maps on sum-free products of spheres

In this article, we study the periodic structure of transversal maps on the product of spheres of different dimensions. In particular, we give sufficient conditions in order that such maps have infinitely many even and odd periods. Moreover, we also provide sufficient conditions for having non-zero Lefschetz numbers of period m for infinitely many m's. We extend these results to transversal maps on rational exterior spaces of rank 1.     

CP-H-extendable maps between Hilbert modules and CPH-semigroups

One may ask which maps between Hilbert modules allow for a completely positive extension to a map acting block-wise between the associated (extended) linking algebras. In these notes we investigate in particular those CP-extendable maps where the 22-corner of the extension can be chosen to be a homomorphism, the CP-H-extendable maps. We show that they coincide with the maps considered by Asadi [4], by Bhat, Ramesh, and Sumesh [9], and by Skeide [28]. We also give an intrinsic characterization that generalizes the characterization by Abbaspour Tabadkan and Skeide [1] of homomorphically extendable maps as those which are ternary homomorphisms. For general strictly CP-extendable maps we give a factorization theorem that generalizes those of Asadi, of Bhat, Ramesh, and Sumesh, and of Skeide for CP-H-extendable maps. This theorem may be viewed as a unification of the representation theory of the algebra of adjointable operators and the KSGNS-construction. Then, we examine semigroups of CP-H-extendable maps, so-called CPH-semigroups. As an application, we illustrate their relation with a new sort of generalized dilation of CP-semigroups, CPH-dilations.     

圆周自映射的一些动力系统性质及其等价条件

本文介绍了近年来关于圆周连续自映射的动力系统性质的一些研究工作，并补充了一些新的结果，从链回归点的角度对圆周连续自映射作了新的探讨。     

Stable manifolds associated to fixed points with linear part equal to identity

We consider maps defined on an open set of having a fixed point whose linear part is the identity. We provide sufficient conditions for the existence of a stable manifold in terms of the nonlinear part of the map.These maps arise naturally in some problems of Celestial Mechanics. We apply the results to prove the existence of parabolic orbits of the spatial elliptic three-body problem.