有界对称域的特征

We give a necessary and sufficient condition for a domain to be biholomorphic to a bounded symmetric domain.     

Characterization of Bounded Symmetric Domain by Carathèodory and Eisenmann-Kobayashi Volume Elements

1 IntroductionClassification of bounded domain is an important problem in several complex variables.The best result was got by E. Cartan. He proved that any boundd symmetric domain must bebiholimorphic to one of the following domains or their topological …     

有界星形域上的Poincaré不等式

本文得到了有界星形域上的Poincar啨不等式 ,证明了Poincar啨域在满足一定条件的拟共形映照下是不变的 .     

一类本性谱有界算子的刻画

设H是一个无限维复Hilbert空间,B(H)表示H上的有界线性算子的全体,并且Φ是从B(H)到自身的线性满射.我们证明了映射Φ是本性谱有界且模紧算子的充分必要条件是Φ(K(H))■K(H)且诱导映射Φ是Calkin代数上的连续同态或连续反同态.     

Successive Pursuit with a Bounded Detection Domain

We study a coplanar model of the successive pursuit of two evaders with unlimited turn rates of the players and a bounded detection domain of a pursuer. Involved in catching the first evader, the pursuer may lose sight of the other. In this case, it must search later for the lost evader in the plane. We describe two guaranteed pursuit strategies obtained as solutions of differential games. Both strategies include a two-stage strategy to shorten to a specified quantity the distance to the nearer evader, and a two-stage strategy to search and capture the other.The strategies are distinguished by their search plans. First, coalition is pursued as a whole. Then, to minimize an uncertainty index, the pursuer approaches the first evader using the strategy of successive pursuit with the unmoved second evader at its last observed position. Subsequently, the pursuer moves directly to that position of the second evader, or according to the more complex plan, alternates between traversing a straight line and arcs of logarithmic spirals. After detection, the remaining evader is captured with the use of a simple pursuit strategy.The barriers fit the strategies. We call them approximate, since they bound the states where the pursuer succeeds with the guaranteed (but not optimal as in the case of ordinary barriers) strategies. These barriers are surfaces of constant values of a special game of degree. The more complex search plan secures a wider winning area.Geometrical interpretations and some numerical results for a set of parameters of the game are provided.     

The Bisymplectomorphism Group of a Bounded Symmetric Domain

We determine the group of diffeomorphisms of a bounded symmetric domain, which preserve simultaneously the hyperbolic and the at symplectic form. *Research partially supported by GNSAGA (INdAM) and MIUR of Italy; MIUR Project “Geometric Properties of Real and Complex Manifolds” (PRIN05). **Research partially supported by GNSAGA (INdAM) and MIUR of Italy; MIUR Project “Geometric Properties of Real and Complex Manifolds” (PRIN05). ***Part of this work was done in July 2007 during a visit of G. Roos at Politecnico di Torino; visit supported by GNSAGA (INdAM) and MIUR of Italy; MIUR Project “Geometric Properties of Real and Complex Manifolds: (PRIN05).     

Cn空间中有界域上一种积分表示

本文应用单位分解的观点及积分表示中核函数的构造理论,得到ln空间中有界域上积分表示的一种抽象的一般形式,根据这种一般形式,可以得到至今许多区域上光滑函数和全纯函数种种已有的抽象公式和具体的积分公式.     

A Characterization of Higher Rank Symmetric Spaces Via Bounded Cohomology

Let M be complete nonpositively curved Riemannian manifold of finite volume whose fundamental group Γ does not contain a finite index subgroup which is a product of infinite groups. We show that the universal cover is a higher rank symmetric space iff is injective (and otherwise the kernel is infinite dimensional). This is the converse of a theorem of Burger–Monod. The proof uses the celebrated Rank Rigidity Theorem, as well as a new construction of quasi-homomorphisms on groups that act on CAT(0) spaces and contain rank 1 elements. Received: September 2007, Accepted: March 2008     

有界对称域上Bloch函数的一个新的特征

本文得到了Cⁿ中有界对称域上Bloch函数的一个新的特征,推广了在单位园盘上的已知结果.     

A Nonhomogeneous Boundary Value Problem for the Boussinesq Equation on a Bounded Domain

In this paper, we study the well-posedness of an initial-boundary-value problem (IBVP) for the Boussinesq equation on a bounded domain,\begin{cases} &u_{tt}-u_{xx}+(u^2)_{xx}+u_{xxxx}=0,\quad x\in (0,1), \;\;t>0,\\ &u(x,0)=\varphi(x),\;\;\; u_t(x,0)=ψ(x),\\ &u(0,t)=h_1(t),\;\;\;u(1,t)=h_2(t),\;\;\;u_{xx}(0,t)=h_3(t),\;\;\;u_{xx}(1,t)=h_4(t).\\ \end{cases} It is shown that the IBVP is locally well-posed in the space $H^s (0,1)$ for any $s\geq 0$ with the initial data $\varphi,$ $\psi$ lie in $H^s(0,1)$ and $ H^{s-2}(0,1)$, respectively, and the naturally compatible boundary data $h_1,$ $h_2$ in the space $H_{loc}^{(s+1)/2}(\mathbb{R}^+)$, and $h_3 $, $h_4$ in the the space of $H_{loc}^{(s-1)/2}(\mathbb{R}^+)$ with optimal regularity.     

有界连通区域上Dirichlet空间及其算子

本文主要讨论了有界连通区域Dirichlet空间上Toeplitz算子的Fredholm性质,计算了符号在C1中的Toeplitz算子的本性谱和Fredholm指标．     

Φ~n空间中有界域上一种积分表示

本文应用单位分解的观点及积分表示中核函数的构造理论,得到~n空间中有界域上积分表示的一种抽象的一般形式,根据这种一般形式,可以得到至今许多区域上光滑函数和全纯函数种种已有的抽象公式和具体的积分公式。     

A Time Domain Characterization of 2-Microlocal Spaces

In Kolwankar and Lévy Véhel, new functional spaces, denoted $K^{s,s}_{x_0}$, were introduced. These spaces characterize the fine local regularity of functions, much in the spirit of 2-microlocal spaces $C^{s,s}_{x_0}$. In contrast with $\C^{s,s}_{x_0}$ spaces, however, $K^{s,s}_{x_0}$ spaces are defined through simple estimations on the pointwise values of the functions. In this work, we generalize the definition of $K^{s,s}_{x_0}$ spaces and prove the equality $C^{s,s}_{x_0}=K^{s,s}_{x_0}$ for $s+s>0$, $s>0$. Using this result, we propose an algorithm able to estimate a part of the 2-microlocal frontier. Experiments on sampled data show that reasonable accuracy is achieved even for difficult functions such as continuous but nowhere differentiable ones. As a by-product, robust estimators of both the pointwise and the local exponents are obtained.     

A New Characterization of the Analytic Radon-Nikodym Property for Bounded S

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Topology of Complete Manifolds with Radial Curvature Bounded from Below

We investigate the topology of a complete Riemannian manifold whose radial curvature at the base point is bounded from below by that of a von Mangoldt surface of revolution. Sphere theorem is generalized to a wide class of metrics, and it is proven that such a manifold of a noncompact type has finitely many ends. Received: December 2005, Accepted: March 2006     

一类完备Riemann流形上的有界调和函数

本文我们将对一类完备Ｒｉｅｍａｎｎ流形上的有界调和函数所组成的线性空间的维数的上界进行估计，同时给出了一个关于测地球体积的Ｂｉｓｈｏｐ－Ｇｒｏｍｏｖ型体积比较定理。     

有界多连通域的具分段连续符号的Toeplitz算子

探讨多连通域的Bergman空间上的具有分段连续符号的Toeplitz算子,刻画了它们的本质谱和Fredholm指标.     

非光滑有界凸域上全纯自映射的随机迭代

该文在经典的Wolff-Denjoy理论的基础上研究C~n中有界严格凸域与有界弱凸域上随机迭代的收敛性问题.给出了有界严格凸域中全纯映射的随机迭代存在内闭一致收敛到边界上的常值映射的子序列的限制条件;而在有界弱凸域中,所给的限制条件强了很多,但全纯映射的随机迭代的收敛性却减弱了.该文所给定理的证明方法可以证明单个解析函数的相应结果的迭代理论.     

Cartan例外域的对合及其有界域的形式

本文给出了复维数为１６的Ｃａｒｔａｎ例外域的对合变换，并由此得到了该域的有界域的形式。