一些蕴含Furuta不等式的算子单调函数的算子不等式

本文研究了算子不等式与算子单调函数之间的联系.利用关于算子单调函数的乘积引理,乘积定理等基本控制原理,给出许多算子不等式,这些不等式可包含正算子理论中应有十分广泛的Furuta不等式.     

一些蕴含Furuta不等式的算子单调函数的算子不等式（英文）

本文研究了算子不等式与算子单调函数之间的联系.利用关于算子单调函数的乘积引理,乘积定理等基本控制原理,给出许多算子不等式,这些不等式可包含正算子理论中应有十分广泛的Furuta不等式.     

正线性算子的Young型逆不等式的一个改进

本文研究了正线性算子的Young型逆不等式的问题.利用算子单调函数以及凸函数的性质,获得了若干带有Kantorovich常数的Young型逆不等式标量形式及相对应的正线性算子的Young型逆不等式的改进形式,推广了现有文献中的结论.     

正线性算子的Young型逆不等式的一个改进（英文）

本文研究了正线性算子的Young型逆不等式的问题.利用算子单调函数以及凸函数的性质,获得了若干带有Kantorovich常数的Young型逆不等式标量形式及相对应的正线性算子的Young型逆不等式的改进形式,推广了现有文献中的结论.     

关于矩阵和算子迹的一组不等式

给出关于半正定矩阵迹和正算子迹的一组不等式,得到与邱贤忠关于实数的不等式的类似结果.     

算子Dunkl-Williams型不等式

在于讨论和经典Dunkl-Williams型不等式相类似的算子不等式,得到了几个算子Dunkl-Williams型不等式,并将其与现有的不等式进行了比较,结果表明,所得的结果是前期结果的推广和改进.     

球面卷积算子逼近

研究d维欧氏空间R~d中单位球面上卷积算子的逼近问题.利用球面乘子理论以及K-泛函与光滑模等价关系,建立一类球面卷积算子逼近的正、逆定理.特别地,给出了逼近的强型逆向不等式,从而揭示了该类球面卷积算子的本质逼近阶.此外,作为应用,给出了球面Jackson-Matsuoka卷积算子与Abel-Poisson卷积算子逼近上、下界的相同阶估计.     

两个正交射影差的范数不等式

设H是一个希尔伯特空间,B(H)表示H上有界线性算子全体构成的集合.P,Q∈B(H)是两个正交射影.运用算子分块技巧给出了||PX-XQ||的一个刻画,在此基础上证明了不等式||P-Q||≤1.进一步运用算子分块技巧与算子谱理论,给出||P-Q||=1以及严格不等式成立的充分条件.最后给出P-Q可逆的一个等价刻画.     

一类算子迹的不等式

将一个算子迹的不等式进行加细,并获得了一个新的算子迹不等式.     

复合算子的双权Poincaré-型不等式

函数形式的Poincaré不等式在偏微分方程、位势分析等领域有着广泛的应用.给出LaplaceBeltrami算子和Green算子复合作用下A-调和张量的双权Poincaré不等式.它是经典Poincaré不等式的自然推广,并为A-调和张量性质的研究提供了有效工具.     

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.     

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.     

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     

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     

Bounds for the zeros of polynomials

Let P(z)=∑↓j=0↑n ajx^j be a polynomial of degree n. In this paper we prove a more general result which interalia improves upon the bounds of a class of polynomials. We also prove a result which includes some extensions and generalizations of Enestrǒm-Kakeya theorem.     

Boundedness of commutators related to Marcinkiewicz integrals on hardy type spaces

In this paper, the authors study the boundedness of the operator [μΩ, b], the commutator generated by a function b ∈ Lipβ(Rn)(0 ＜β≤ 1) and the Marcinkiewicz integrals μΩ, on the classical Hardy spaces and the Herz-type Hardy spaces in the case Ω∈ Lipα(Sn-1)(0 ＜α≤ 1).     

Generalization of the interaction between Haar approximation and polynomial operators to higher order methods

In applications it is useful to compute the local average empirical statistics on u. A very simple relation exists when of a function f（u） of an input u from the local averages are given by a Haar approximation. The question is to know if it holds for higher order approximation methods. To do so, it is necessary to use approximate product operators defined over linear approximation spaces. These products are characterized by a Strang and Fix like condition. An explicit construction of these product operators is exhibited for piecewise polynomial functions, using Hermite interpolation. The averaging relation which holds for the Haar approximation is then recovered when the product is defined by a two point Hermite interpolation.     

Jacobi polynomials used to invert the laplace transform

Given the Laplace transform F(s) of a function f(t), we develop a new algorithm to find an approximation to f(t) by the use of the classical Jacobi polynomials. The main contribution of our work is the development of a new and very effective method to determine the coefficients in the finite series expansion that approximation f(t) in terms of Jacobi polynomials. Some numerical examples are illustrated.