矩量定理的一种推广

矩量定理是线性泛函分析中的一个重要定理,有着广泛的应用.它研究的是线性赋范空间上一类连续线性泛函的存在性条件,这类连续线性泛函要求在给定的n个线性无关元上取指定值,并且,该泛函的范数不大于某个预先给定的界限.著作[3]中,在研究分布参数系统控制理论时,将其推广,把给定的有限个线性无关元扩充为无限的可数个线     

LF拓扑线性空间上Fuzzy线性泛函的连续性

文（４）中给出了Ｘ（Ｌ）上的模糊线性算子的定义。作为其特例，本文证明了ＬＦ拓扑线性空间上模糊线性泛函连续性的几个等价命题和模糊线性泛函的Ｈａｈｎ－Ｂａｎａｃｈ延拓定理，进而给出了ＬＦ拓扑线性空间上存在非零连续模糊线性泛函的一个充要条件。     

赋范锥到赋范线性空间的嵌入定理与赋范锥上的Hahn-Banach定理

研究赋范锥到赋范线性空间的嵌入问题与赋范锥上连续线性泛函的Hahn-Banach正延拓问题.第一部分采用几何方法直接证明赋范锥到赋范线性空间的嵌入定理.对于给定的赋范线性空间中的凸锥,通过引进凸锥的"锐性模".第二部分研究由锥范数导出的延拓范数与原范数的等价关系.第三部分给出赋范锥上连续线性泛函的Hahn-Banach正延拓定理.     

再生核希尔伯特空间连续线性泛函的范数及其应用北大核心

考虑了再生核希尔伯特空间连续线性泛函范数的表示,得到了用其范数平方等于该线性泛函连续两次作于再生核的简明表示.对于常见的Sobolev-Hibert空间而言,其再生核则可用截幂函数来表示,从而得到Sobolev-Hibert空间上连续线性泛函范数的简洁表示,以新视角解释和简化了文献中的现有结果.     

非局部凸拓扑线性空间中的Hahn Banach延拓性

1 序 众所周知,Hahn(1926)和Banach(1929)曾经在赋范空间中给出过一个十分重要的有关连续线性泛函的延拓定理: H.-B.定理 设X为赋范空间,X_0为X的一个线性子空间,那么,对任意连续线性泛函     

赋范线性空间中强增生算子方程的迭代解

在去掉｜（1-A）xn｜有界的条件下,在实赋范线性空间中研究了强增生映象零点的最速下降法的迭代逼近问题,从而改进和发展了近期的相关结果．     

关于赋范空间上连续自映射的回归点

在赋范空间中讨论回归点的性质,主要得到了结果：（1）如果,是序列紧赋范空间X上的连续双射,x是f的任一回归点,则对于任意整数N〉0都存在f的回归点x0∈X使得f^n（x0）=x;（2）序列紧赋范空间上连续自映射的回归点集是f的强不变子集;（3）如果f是局部连通赋范空间X上的连续自映射,则f的每一个回归点或是类周期点或是类周期点的聚点．作为推论,在实直线段上得到了类似的结论．     

单位球面上的等距延拓

该文研究了实赋范空间的单位球面上的等距算子延拓问题. 为此, 作者定义一个新的空间E^#, 称之为正齐性对偶空间, 并且研究了E^#上的一个新的拓扑σ(E^#, E). 从而, 作者就可以证明实赋范空间的单位球面上的一类满等距算子可以线性延拓到全空间上.     

内积空间的一些特征

在本文中始终假设 E 是一个实赋范线性空间,S(E)={x∶‖x‖=1,x∈E}.K.Suudaresan 在〔1〕中提出的关于内积空间的第一个特征是:E 是内积空间的充要条件是对于任何 p>2以及任意的 x,y∈E 有     

非线性一致同时逼近

设Ω是紧Ｈａｕｓｄｏｒｆｆ空间,Ｃ（Ω）表示定义在Ω上取值于实数域的所有实连续函数全体组成的空间,在Ｃ（Ω）上定义一致范数则Ｃ（Ω）构成一个Ｂａｎａｃｈ空间．定义其中 ｜｜· ｜｜Ｂ是Ｒｍ中给定的范数． 设Ｇ是Ｃ（Ω）的一个非空子集,ｆ１,…,ｆｍ是Ｃ（Ω）中给定的ｍ个函数．若存在ｆ∈Ｇ,满足那么称这样的ｆ是Ｇ对Ｆ的最佳一致同时逼近,其全体记为ＰＧ（Ｆ）． 近年来．最佳同时逼近问题作为单元最佳逼近问题的推广,受到了广泛的关注．文［１－６］在一般的Ｂａｎａｃｈ空间中研究了各种意义下的最佳同时逼近的特征…     

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.     

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.     

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.     

CONTENTS OF VOLUME 30

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Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with     

Journal of Mathematical Research with Applications Guide for Authors

正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].     

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.