Hilbert空间H中带符号广义框架的一个刻画

本文研究了可分的Hilbert空间H中带符号广义框架,利用算子理论方法,给出了H中一族向量{hm}m∈M是一个带符号广义框架当且仅当带符号广义框架的框架算子的正部S 和负部S-是有界线性算子,讨论了H中带符号广义框架的框架算子S的可逆性,并且得到了H中每个向量f关于带符号广义框架{hm}m∈M和其对偶带符号广义框架{~hm}m∈M的表示式.     

关于广义Jacobi权的Lebesgue函数的估计

本文证明了由广义Ｊａｃｏｌｂｉ权产生的Ｌｅｂｅｓｇｕｅ函数在（－１,１）中任意固定内闭区间τ上的估计为Ｏ（ｌｎｎ）,这个结果改进了「３」中在一般抽象权时给出的结论     

ON THE ZEROS OF QUOTIENTS OF BESSEL FUNCTIONS

1. The Main ResultsIn this paper we establish the following result concerning the Bessel functions Im(x):Theorem 1.1. (i) For any m ≥2 there exists a unique positive solution x=xm of theequationwhere(ii) If 2≤ｌ < m, thenThis theorem is used in the study of free boundary problems[1]The following result will be used in the proof of (1.3):Theorem 1.2. The function G(x) is concave for 0 相似文献   

广义H-矩阵的乘积的性质

1 引言 广义M-矩阵和广义H-矩阵的理论在许多实际问题的研究中有着非常重要的作用,如欧拉方程数值求解中出现的线性系统的块迭代法的收敛性问题,以及动力系统的研究等.     

关于广导算子的零空间

本文讨论了两类广义导算子δＡＢ（ｘ）＝Ａｘ－ｘＢ和τＡＢ（ｘ）ＡｘＢ－Ｘ，并给出了一些成立的充分必要条件     

关于图的符号控制数的下界

图的符号控制数的研究有许多应用背景，但图的符号控制数的计算是NP完全问题，因而确定其上下界有重大意义。本文在[5]的基础上，引进了新参数δ^*(G)，全面改进了[5]所给出的符号控制数的下界，并给出了一些可达下界的图。     

ON THE ESTIMATION OF GENERALIZED LEBESGUE CONSTANT AND MODULUS OF GENERALIZED SINGULAR QUADRATURE FORMULAS AND ITS APPLICATION

This article, first gives the estimaties of two modulus, namely, generalized Lebesgue constant and modulus of generalized singular integral quadrature formulas, then applies them to obtain the error bounds of the operator BLmp to the operator B.     

ON THE GENERALIZED RESOLVENT OF LINEAR PENCILS IN BANACH SPACES

Utilizing the stability characterizations of generalized inverses of linear operator, we investigate the existence of generalized resolvent of linear pencils in Banach spaces. Some practical criterions for the existence of generalized resolvents of the linear pencil λ→ T λ S are provided and an explicit expression of the generalized resolvent is also given. As applications, the characterization for the Moore-Penrose inverse of the linear pencil to be its generalized resolvent and the existence of the generalized resolvents of linear pencils of finite rank operators, Fredholm operators and semi-Fredholm operators are also considered. The results obtained in this paper extend and improve many results in this area.     

SINGULAR INTEGRAL OPERATORS IN L~2 SPACES ASSOCIATED WITH THE GENERALIZED JACOBI WEIGHTS

In this paper, a kind of new definitions of singular integral operators in the weighted L2 space with the generalized Jacobi weights are given, then the boundedness in the weighted L2 space, the relationships between these operators and the classic singular integral operators are proved. For the convenience in the later use, similar results in the L2 space with Jacobi weights are given.     

COMMUTATORS OF GENERALIZED HARDY OPERATORS ON HOMOGENEOUS GROUPS

Let G be a homogeneous group. The author considers the boundedness of commutators generated by the generalized Hardy operators and CMO（G） functions on Herz spaces in the setting of homogeneous group. This article extends some known results.     

PERTURBING FAMILIES OF GENERALIZED LYAPUNOV FUNCTIONS AND RELATIVE STABILITY IN TERMS OF TWO MEASURES

ＰＥＲＴＵＲＢＩＮＧＦＡＭＩＬＩＥＳＯＦＧＥＮＥＲＡＬＩＺＥＤＬＹＡＰＵＮＯＶ　ＦＵＮＣＴＩＯＮＳＡＮＤＲＥＬＡＴＩＶＥＳＴＡＢＩＬＩＴＹＩＮＴＥＲＭＳＯＦＴＷＯ　ＭＥＡＳＵＲＥＳＳｈａｎｇＬｉｊｕｎ（商立军）（ＴｈｅＦｏｕｒｔｈＭｉｌｉｔａｒｙＭｅ...     

环Z2l上广义Bent函数的稳定性

文献「４」为研究密钥流序列的线性复杂度稳定性和使一些流密码能抗ＢＡＡ（最佳仿射逼近）攻击,提出Ｂｅｎｔ函数稳定性概念,文献「７」研究了素域Ｚｐ上广义Ｂｅｎｔ函数的稳定性及其构造,并指出当ｍ是合数时,ｍ值广义Ｂｅｎｔ函数并不都有稳定性,本文进一步在环Ｚ２＾ｌ（ｌ〉１）上提出了广义Ｂｅｎｔ函数稳定性的概念,综合应用谱、概率和代数数论的方法考察了稳定的概率意义,给出了稳定函数的概率判别条件,提供了构造稳     

一类解析算子函数空间上的复合算子

本文用算子函数论的方法，研究了解析算子函数的Banach空间X，X0上的复合算子．给出此复合算子为有界的条件，并刻划了此复合算子在X0上为紧的特征．     

ON THE CONSTRUCTION OF MAJOR AND MINOR FUNCTIONS

In this paper,we construct directly absolutely continuous major and minor functions of a function which is Lebesque integrable ,and we also construct directly continuous major and minor functions of a function which is Henstock-Kurzweil integrable.     

ON J-SELFADJOINT EXTENSION OF THE PRODUCT OF TWO nTH-ORDER J-SYMMETRIC ORDINARY DIFFERENTIAL OPERATORS ON [a,b]

The problem of J-selfadjointness of the product of two nth-order J-symmetric operators on [a,b] is studied. We give a condition to ensure that the product operator is a J-selfadjoint extension.     

拟可加测度空间上广义Sugeno积分的收敛性

在拟可加测度空间上通过引入拟乘算子重新定义广义Sugeno积分,针对依拟可加测度收敛的函数列,应用诱导算子和拟乘算子的运算性质讨论和分析广义Sugeno积分的收敛性,进而获得了这种广义Sugeno积分的单调增收敛定理.     

关于两个P-值逻辑函数的和函数的Chrestenson谱公式

类似于两个布尔函数的和函数的ｗａｌｓｈ谱公式,本文给出了两个３－值、５－值、７－值逻辑函数和函数的Ｃｈｒｅｓｔｅｎｓｏｎ谱公式。     

关于实轴上多解析函数Riemann边值问题的可解性

本文研究了实轴上具有不同因子的多解析函数的Riemann边值问题的可解性．利用所谓的转化法．建立了Riemann问题的可解性与其相联问题的解之间的关系。该结果推广了解析函数的相应理论。     

关于连续线性算子广义预解集的某些结果

讨论了Banach 空间上连续线性算子$T$ 的广义预解集的相关结果,证明了:若$\lambda_0\in\rho_G(T),$ 当~$|\lambda-\lambda_0|<\gamma(T_{\lambda_0})$ 时,$\lambda\in\rho_G(T);$ 与~$\lambda\in\rho_G(T)$ 等价的条件:当~$T_n\to T, 0\in \rho_G(T_n),则~$0\in\rho_G(T);$ 以及$T$ 的柱心~$C_O(T)$ 在数量扰动下的不变性.     

ON THE CENTER OF GENERALIZED LIENARD SYSTEM

This paper discusses the local and global center of the generalized Lienard system, gives two theorems which extend and improve the relative results of [1]-[3]. Moreover the lemmas in this paper are also useful to the study for the oscillation, stability and the existence of limit cycles of the generalized Lienard system.