Hilbert C*-模中K-框架的一些性质

本文将Hilbert空间中K-框架的概念推广到Hilbert C*-模中,得到了Hilbert C*-模中K-框架的几个等价刻画.另外给出条件使得Hilbert C*-模中的K-框架去掉某个元素后的剩余集仍是K-框架.     

Hilbert C~*-模中K-框架的对偶性

本文研究Hilbert C~*-模中K-框架的对偶问题.利用算子理论方法,获得Hilbert C~*-模中K-对偶Bessel序列的一些刻画,推广了Hilbert空间中K-框架的对偶理论.     

Hilbert W*-模上的广义框架

本文研究了Hilbert W*-模上的广义框架.运用了算子理论的方法,得出了Hilbert W*-模上的广义框架的一些结果,与标准离散Hilbert C*-模框架的一些结果是相似的.     

Hilbert C*-模上框架(强)可补的充要条件

Hilbert C*-模上框架的框架变换的实质是将该模进行膨胀,使得该框架变换的值域存在标准正交基,以便于Hilbert C*-模上不同框架之间关系的研究.受此启发,本文引入了Hilbert C*-模上框架(强)可补的概念,给出并证明了Hilbert C*-模上有限个框架(强)可补的充要条件.     

Hilbert C~*-模中融合框架的新刻画

观察到Hilbert C*-模中融合框架原定义的不合理性,然后通过权重集的选取将其改进,得到融合框架的新定义并给出其等价形式.特别地,利用算子理论方法得到了Hilbert C*-模中融合框架的一个新刻画.     

Hilbert K-模上酉群的框架表示

本文主要研究了Hilbert K-模上酉群的框架表示的一些基本性质，联系框架的强不相交性，得到了Hilbert K-模上酉群的框架表示的重数是有限的．     

Hilbert空间中的广义K-框架

通过引入广义K-框架和广义K-原子系统给出了Hilbert空间上有界线性算子K的值域的一种新的重构方式.广义K-框架是Hilbert空间中广义框架和K-框架概念的一种新的推广.为了建立基于广义K-框架的元素重构理论,广义K-对偶对和广义逼近K-对偶对的概念被引入.此外,广义K-框架和广义K-原子系统之间的关系,广义K-对偶对的存在条件以及广义K-对偶对和广义逼近K-对偶对之间的联系等问题被深入地讨论和研究.     

K-框架和紧K-框架的算子扰动的稳定性

该文在Hilbert 空间中讨论K-框架和紧K-框架在算子扰动中的稳定性.首先给出K-框架经过有界线性算子T 扰动后为K-框架的充要条件,其次讨论了用两个Bessel 序列或者两个K-框架构造新的K-框架的方法,最后给出用两个Bessel 序列构造紧K-框架的充要条件.这些结果推广和改进了由Christensen和Ca...     

Hilbert C~*-模中K-Fusion框架的刻画

首先通过权重集的选取改进了HilbertC~*-模中fusion框架的原有定义.然后将K-fusion框架的概念由Hilbert空间推广到Hilbert C~*-模中,并且利用算子理论方法得到了Hilbert C~*-模中K-fusion框架的一些等价刻画.     

酉系统中的受控K-融合框架生成子

本文引入了酉系统中的(C,C’)-受控融合框架生成子和(C,C’)-受控K-融合框架生成子的概念,它们都是框架的推广.研究了酉系统中的(C,C’)-受控融合框架生成子和融合框架生成子之间的关系,并给出了(C,C’)-受控K-融合框架生成子的一些刻画.此外,探讨了Hilbert空间H的一个闭子空间成为(C,C’)-受控融合框架生成子以及(C,C’)-受控K-融合框架生成子的条件.     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.     

A unified approach to certain problems of best local approximation

In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables. Our approach extends and unifies several problems concerning best local multi-point approximation in different norms.     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

<正>August 10-14,2015Beijing,ChinaThe International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists     

Towards Excellence in Science Chinese Academy of Sciences

<正>May 26,2014,Beijing Science is a human enterprise in the pursuit of knowledge.The scientific revolution that occurred in the 17th Century initiated the advances of modern science.The scientific knowledge system created by