上三角无穷维Hamilton算子的剩余谱

将点谱划分为四个部分,得到上三角无穷维Hamilton算子的点谱σ_p(H)关于虚轴对称的充要条件.在此基础上,结合无穷维Hamilton算子的谱结构,得到无穷维Hamilton算子剩余谱的完全描述,从而实现了利用其内部算子刻画剩余谱.     

一类无穷维Hamilton算子的谱估计

研究了一类无穷维Hamilton算子近似点谱的范围.进而,当此类无穷维Hamilton算子是辛自伴算子时,给出了它的谱范围.并刻画了分块对角算子的近似点谱.最后举例说明了判别准则的有效性.     

无穷维Hamilton算子的近似点谱

本文研究了无穷维Hamilton算子的近似点谱.得到了无穷维Hamilton算子的近似点谱和谱集之间的关系,从而给出无穷维Hamilton算子的近似点谱关于虚轴对称的充分必要条件.     

无穷维Hamilton算子的谱结构

研究无穷维Hamilton算子的谱结构. 得到无穷维Hamilton算子的谱、点谱和剩余谱之并集和连续谱均关于虚轴对称. 此外, 还证明了无穷维Hamilton算子的剩余谱不含有任何关于虚轴对称的点对, 从而利用点谱完全刻画了剩余谱. 作为谱结构的应用, 得到一类无穷维Hamilton算子剩余谱为空集的若干充分必要条件.     

一类无穷维Hamilton算子的谱刻画及其可逆性

研究了定义域为对角形的上三角无穷维Hamilton算子:H=的谱刻画及其可逆性;当A的剩余谱不含关于虚轴对称的点时,H的谱等于A的谱与A的谱关于虚轴对称分支的并集,并得到了H的预解集为空及其可逆的充要条件;作为结论的应用,得到当A为无穷维Hamilton算子时,H的点谱、剩余谱、连续谱和谱分别等于A的点谱、剩余谱、连续谱和谱.     

2×2上三角无界算子矩阵的谱

本文研究了Hilbert空间中的对角定义的2×2上三角闭线性算子矩阵的谱、近似点谱、亏谱和本质谱的性质,进而得到了算子矩阵的谱、近似点谱和亏谱分别等于对角算子的谱、近似点谱和亏谱的并集的充要条件;还得到了算子矩阵的本质谱等于对角算子的本质谱的并集的充分条件.作为应用,本文还得到了对角定义的上三角无穷维Hamilton算子的谱性质.     

一类无穷维Hamilton算子的谱

研究了一类无穷维Hamilton算子的近似点谱及本质谱.进而通过无穷维Hamilton算子内部元素的乘积的谱对整体谱进行了刻画,最后证明了结论的正确性.     

一类无穷维Hamilton算子谱的刻画

本文讨论了一类无穷维Hamilton算子谱问题,由于无穷维Hamilton算子是非自伴的算子矩阵,对它的谱的讨论比较困难,我们利用无穷维Hamilton算子的特殊结构,将无穷维Hamilton算子的谱问题转化为它的元素算子的某种组合的谱问题,得到了一个充分必要条件,在一定程度上简化了该类无穷维Hamilton算子谱的计算.     

上三角无穷维Hamilton算子特征值的代数指标

无穷维Hamilton算子特征函数系是否完备与其代数指标有关,研究了上三角无穷维Hamilton算子特征值的代数指标问题,基于主对角元的特征值和特征向量的某些性质,得到上三角无穷维Hamilton算子的几何重数和代数重数.     

一类缺项算子矩阵的谱扰动

有界线性算子的点谱和剩余谱分别可进-步细分为两类:σ_(p1),σ_(p2)和σ_(r1),σ_(r2).设H,K为无穷维可分的Hilbert空间,本文将对于给定的A ∈B (H),B ∈B(K),给出了缺项算子M_C=(AC/OB)关于分类后所得四种谱的扰动结果.     

A multidimensional central limit theorem with speed of convergence for axiom a diffeomorphisms

Let T:X → X be an Axiom A diffeomorphism,m the Gibbs state for a Hlder continuous function ɡ. Assume that f:X → R^d is a Hlder continuous function with ∫_X^fdm = 0.If the components of f are cohomologously independent, then there exists a positive definite symmetric matrix σ²:=σ² （f ） such that S^fn √ n converges in distribution with respect to m to a Gaussian random variable with expectation 0 and covariance matrix σ² . Moreover, there exists a real number A > 0 such that, for any integer n ≥ 1,Π( m*（ 1√ nS f n ）,N （0,σ² ） ≤A√n, where m*（1√ n S^fn）denotes the distribution of 1√ n S^fn with respect to m, and Π is the Prokhorov metric.     

含有奇异位势和临界指数的拟线性椭圆方程的G-对称解

本文讨论一类奇异拟线性椭圆型方程
-div(|x|^-ap|▽u|^p-2▽u)=μ+h(x)/|x|^(a+1)p|u|^p-2u+k(x)|u|^p-2u/|x|^bq,x∈R^N,
其中1 < p < N, 0 ≤ a < N-p/p, a ≤ b < a + 1, 0 ≤ μ < μ = (N-p/p-a)^p, q=p^*(a, b) = Np/N-(1+a-b)p,h 和k 是R^N上的连续有界函数, 且关于O(N) 的闭子群G满足某些对称性条件. 应用变分方法和Caffarelli-Kohn-Nirenberg 不等式, 在h与k满足适当条件下, 证得了一些G-对称解的存在性和多重性结果.     

上三角无穷维Hamilton算子点谱的对称性

In this paper, by using characterization of the point spectrum of the upper triangular infinite dimensional Hamiltonian operator H, a necessary and sufficient condition is obtained on the symmetry of σP（A） and σ1/P（-A^＊） with respect to the imaginary axis. Then the symmetry of the point spectrum of H is given, and several examples are presented to illustrate the results.     

Holomorphic mappings of a strip into itself with bounded distortion at infinity

A class of holomorphic self-mappings of a strip which is symmetric with respect to the real axis is studied. It is required that the mappings should boundedly deviate from the identity transformation on the real axis. Distortion theorems for this class of functions are obtained, and domains of univalence are found that arise for certain values of the parameter characterizing the deviation of the mappings from the identity transformation on the real axis.     

除数和函数对平方补数的均值

对于任意正整数n的平方补数c（n）,研究了其除数和函数σ（c（n））均值的渐近性,并利用解析方法得到了一个渐近公式。     

一类Schrǒdinger算子的谱分析

本文研究了Hilbert空间L^2（R^2）上由势函数V（x）（V≥0,连续）给出的一类Schrǒdinger算子H=-△＋V的谱。本文的主要结果：（1）H的谱σ（H）不会出现本性谱与离散谱交替出现的情况,其谱要么是离散的,要么从infσcos（H）开始全是本性谱;（2）lim‖x‖→∞V（x）=∞是σcos（H）=φ的充要条件。（3）借助于讨论H的Zhis-lin谱,在一定的条件下。lim‖x‖→∞V（x）=0是σcos（H）=[∞,0）的充要条件。我们还提出了几个没有解决的问题。     

An estimate of the error of the linearized equations of motion of an axisymmetric projectile

An estimate is obtained, by small-parameter methods, of the error of the solution for the system of equations of motion of a projectile in the atmosphere, linearized for small angles of attack with respect to the variables describing the angular oscillations of the axis of symmetry, compared with the solution of the initial non-linear system for the same initial conditions.     

Analytic construction of the near field in a transonic flow near a thin axisymmetric body

A solution of the axisymmetric problem of unsteady transonic flow around thin bodies of revolution is proposed in the form of a double series expansion in powers of the distance to the axis of symmetry and its logarithm in a neighborhood of a given point at the symmetry axis. Chains of recurrence equations are obtained for the coefficients of the series. The convergence of the constructed series is proved by the method of special majorants. The theorem of existence and uniqueness of the solution to the boundary-value problem for a nonlinear partial differential equation with a singularity at the symmetry axis is obtained in the asymptotic model of unsteady transonic flow under consideration. Thereby the application of the proposed series is justified to the problems of unsteady transonic flow around thin axisymmetric bodies with a drift of the nonpenetration condition onto the symmetry axis. Hence, these series can be used in numerical-analytical methods and model computations.     

Hardy空间上解析Toeplitz算子的局部谱

考察Hardy空间H^2（T）上的解析Toeplitz算子的局部谱,得到的主要结果是：当φ∈H^∞（T）时,A↓∈H^2（T）,x≠0,σTφ（x）=σ（Tφ）．     

Generating groups of isometries of the line using non-standard metrics

In this article, a simple exercise for finding groups isomorphic to the symmetry group of the real line is presented. A mechanism for producing metrics on the real line is used to construct the group elements, and these transformations, by construction, are isometries with respect to the generating metric.