Krein空间中无穷维Hamilton算子的极大确定不变子空间的存在性问题

本文研究了不定度规空间空间中的无穷维Hamilton算子.利用Plus算子存在极大不变子空间的性质,获得了无穷维Hamilton算子在Krein空间中存在极大确定不变子空间的充分条件.     

广义球面平均算子在α-模空间的导数估计

本文研究了广义球面平均算子S^γ在α-模空间的导数估计,即算子?^βS^γ在α-模空间的有界性,该算子在调和分析以及各应用分支中都具有一定的理论价值.本文首先研究了该算子在模空间的有界性,由于模空间的分解方式具有较好的性质,本文通过精细的计算和格点估计得到了该算子在模空间全指标范围有界的充要条件.随后,本文研究了该算子在一般的α-模空间的有界性,得到了有界性成立的充分条件和必要条件.     

Banach空间值鞅上的拟局部算子

本文研究了拟局部算子在几个Banach空间值鞅空间上的有界性.给出了几个有界性定理,证明了鞅空间的简单原子分解.得到几个极大算子和p均方算子的一系列鞅不等式以及鞅空间的包含关系.     

次线性算子在Herz型Hardy空间上的有界性

本文得到了一类次线性算子在Herz型Hardy空间上的有界性判定条件,该算子包括调和分析中许多重要的算子,同时还证明了Bochner-Riesz算子在Herz型Hardy空间上的有界性.     

加权双线性Hardy算子在加幂权L~p空间中的最佳常数

本文研究了加权双线性Hardy算子和加权双线性Cesaro算子在加幂权L~p空间中的有界性,精确得到了这两类算子在加幂权Lp空间中的算子范数.作为应用,得到了双线性Riemann-Liouville算子和双线性Weyl算子的最佳常数.     

Hilbert空间上的预框架算子

预框架算子是算子理论应用于框架理论研究中的一个重要算子.在本文中我们将讨论预框架算子在Hilbert空间的框架构造以及框架变换和对偶框架方面的一些应用.特别地,我们得到了Hilbert空间上两框架之和是和空间上的框架以及保持框架与对偶框架某些性质的变换的算子论刻画.     

广义f-投影算子的稳定性及其应用

在Banach空间中,本文研究广义f-投影算子关于集合扰动的稳定性.作为应用,本文在Banach空间中运用广义f-投影算子解决了一类广义变分不等式问题.     

解析算子函数空间上的复合算子理论初步

本文将经典Hardy空间上复合算子的理论、方法应用到解析算子函数空间上,给出了解析算子函数空间的几个基本性质及复合算子的有界性条件.     

LBRAGIMOV-GADJIEV-DURRMEYER算子在ORLICZ空间内的逼近性质

本文研究了lbragimov-Gadjiev-Durrmeyer算子在Orlicz空间内的逼近问题.借助了Jensen不等式,H?lder不等式,K泛函,光滑模等工具,获得了lbragimov-Gadjiev-Durrmeyer算子在Orlicz空间内的逼近度,以及该算子的加权逼近,推广了lbragimov-Gadjiev-Durrmeyer算子在L_p空间中的逼近度及加权逼近.     

单位球加权Bergman空间上的乘法算子

函数空间上的乘法算子是包含许多重要算子的算子类,本文主要研究了单位球加权Bergman空间上乘法算子的性质.     

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.     

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.     

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.     

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     

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).     

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.     

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.