ON THE CONVERGENCE OF APPROXIMATION TO CAUCHY SINGULAR INTEGRALS BY WAVELETS

本文讨论了用周期小波对Ｈｏ．．ｌｄｅｒ空间进行的特征刻划，给出了Ｈｏ．．ｌｄｅｒ空间中的若干小波逼近性质，证明了用周期小波逼近Ｃａｕｃｈｙ型奇异积分时的一些收敛定理．     

ON THE COMMUTATIVITY OF MULTIPLE SERIES AND BASIC SEQUENCE

Let X be a Banach space and {e_j}_(j=1)~∞ be a sequence in X. The author showsthat {e_j}_(j=1)~∞ is a basic sequence if and only if ∑_(n=1)~∞, r_nα_(nj) converges for every j≥1 and∑_(n=1)~∞ r_n ∑_(j=1)~∞, α_(nj)e_j=∑_(j=1)~∞,(∑_(n=1)~∞ r_nα_(nj))e_j holds for every choice of scalar variables{α_(nj)} such that ∑_(j=1)~∞ α_(nj)e_j converges for each n≥1 and any choice of scalar variables{r_n} such that ∑_(n=1)~∞ ∑_(j=1)~∞, r_nα_(nj)e_j converges. Moreover, some applications about theresult are given.     

三角级数一致收敛性问题在复空间的完整推广

本文研究了三角级数在复空间中的一致收敛性问题.利用Abel变换等方法,获得了三角级数在复空间中满足上确界有界变差(SBVS)条件下一致收敛的充分必要条件,推广了Korus在实空间中的结论.     

Orlicz-Pettis Type Theorems via Strong p-Cesàro Convergence

We obtain a new version of the Orlicz-Pettis theorem within the frame of the strong p-Cesàro convergence.     

不变的赋值函数与Cauchy投影公式(英文)

本文研究了Rn中凸集上不变的赋值函数与凸体的投影问题.利用赋值函数的方法,我们获得了凸体在任意维平面上投影的Cauchy公式和Kubota公式,这些结果推广了经典的Cauchy公式和Kubota公式.     

CONVERGENCE AND GROWTH OF MULTIPLE DIRICHLET SERIES

This article investigates the convergence and growth of multiple Dirichlet series. The Valiron formula of Dirichlet series is extended to n-tuple Dirichlet series and an equivalence relation between the order of n-tuple Dirichlet series and its coefficients and exponents is obtained.     

Euler级数的收敛性与组合学技巧

通过优序列方法，建立了Ｅｕｌｅｒ级数，即反函数的幂级数的收敛性，而且，我们发现Ｅｕｌｅｒ级数的系数和具有ｎ个元素的Ｓｃｈｒｏｄｅｒ系的个数之间的联系，以及Ｅｕｌｅｒ级数收敛半径的确切下界可通过相应的指母函数的收敛半径得到 。     

关于在∧-∨复合之下格矩阵的收敛性

本文研究了在复合∧-∨下格矩阵幂序列的收敛性，利用格中∧与∨运算的特性，获得了格矩阵幂序列的一些性质，证明了在∧-∨复合下．任一个几乎非自反格矩阵的幂序列是递减与收敛的．     

PERTURBATION THEOREMS ON HERMITIAN MATRICES AND NEARLY HERMITIAN MATRICES

The problem of relating the eigervalues of an n×n Hermitian matrix to those of its Rayleigh-Ritz approximation is considered. The same residual bound for unitarily invariant norms on Hermilian matrices is obtained even without the orlhonormal and Rayleigh-Ritz assumptions in Stewart and Sun's book [9,Theorem IV. 4.14]. The result can also be extended to nearly Hermitian matrices.     

迹非零布尔矩阵的幂敛指数集

本文给出了恰含d个非零对角元的n阶布尔矩阵类（1≤d≤n)的幂敛指数集的一个明显表达式。     

单位圆周上广义Fourier积分的收敛性

本文研究了复平面单位圆上的广义Fourier积分.利用经典的Fourier分析的结果和Carleson定理,以及复平面上解析函数在高阶导数下直角坐标和极坐标之间的关系,我们得到了前面定义的广义Fourier积分的一个收敛定理,从而推广了直线上经典Fourier积分的收敛结果.     

恰有t行含对称正元的布尔方阵的幂敛指数的估值

设Ｄｎ，２（ｔ）为恰有ｔ行含对称正元的ｎ阶布尔方阵的集合，２≤ｔ≤ｎ。本文证明了，对于任给Ａ∈Ｄｎ，２（ｔ），幂敛指数ｋ（Ａ）≤∫（ｎ－ｔ－１）＾２＋１，３ｎ－ｔ－２，当ｔ≤ｎ－［３＋√８ｎ－７／２］当ｔ〉ｎ－［３＋√８ｎ－７／２］，这里［ｘ］表示不小于ｘ的最小整数。同时，我们还证明了这个界是可以达到的，并且对Ｄｎ，２（ｔ）的极矩阵集合作了部分刻划。     

泛Clifford分析中无界域上的Cauchy积分公式和Cauchy-Pompeiu公式

本文研究了泛Clifford分析中的Cauchy积分公式和Cauchy-Pompeiu公式.通过引入修正的Cauchy核,得出了取值在泛Clifford代数上的两公式在无界域上的表达式.此两公式是有界域上的相应结果的推广,并为研究无界域上的边值问题打下了基础.     

基于第二类Chebyshev多项式的双正交级数及共轭级数(英文)

记Un（z）是第二类Chebyshev多项式，伴随函数，这里讨论基于的双正交级数和其共轭级数的部分和逼近问题。     

圆盘定理的改进与弱连对角占优矩阵

本文对圆盘定理进行了改进，给出了特征值分布新的估计，由此引出了弱连对角占优矩阵，讨论了其基本性质，重点分析了该类矩阵的逆与分裂特征，证明了在该类矩阵条件下Ｈ－相容分裂是收敛分裂，并给出迭代矩阵谱半径的上界及ＳＯＲ算法中参数ω的选取范围。     

几个矩阵范数不等式及其在谱扰动中的应用

1　引　　言在 [5]中 ,孙继广研究了正规矩阵的谱扰动 ,给出了一个Ｈｏｆｆｍａｎ Ｗｉｅｌａｎｄｔ(此后简记为Ｈ -Ｗ )型扰动定理 [6 ]将 [5]中结果加以推广 ,得到了可对角化矩阵的相应扰动定理 近年来 ,这方面的研究工作又取得了一些新的成果[2 ] [7] 在本文中 ,我们将建立几个矩阵范数不等式 ,然后将它们用于可对角化矩阵 (正规矩阵 )的谱扰动 ,导出几个新的Ｈ Ｗ型扰动定理 ,并与有关结果作了比较 本文采用下列记号 :Ｃｎ×ｎ表示ｎ×ｎ复矩阵的全体 ,ＡＨ 表示矩阵Ａ的共轭转置 ,σｊ(Ａ)表示矩阵Ａ的某个奇异值 ,ｄｉａｇ(γ1,……     

UNIFORM CONVERGENCE AND SEQUENCE OF MAPS ON A COMPACT METRIC SPACE WITH SOME CHAOTIC PROPERTIES

Recently, C. Tain and G. Chen introduced a new concept of sequence of time invariant function. In this paper we try to investigate the chaotic behavior of the uniform limit function f ： X →X of a sequence of continuous topologically transitive （in strongly successive way） functions fn ： X →X, where X is a compact interval. Surprisingly, we find that the uniform limit function is chaotic in the sense of Devaney. Lastly, we give an example to show that the denseness property of Devaney＇s definition is lost on the limit function.     

SOME REMARKS ON HOLOMORPHIC FUNCTIONS AND TAYLOR SERIES IN Cn

Some previous results on convergence of Taylor series in Cn [3] are improved by indicating outside the domain of convergence the points where the series diverges and simplifying some proofs. These results contain the Cauchy-Hadamard theorem in C. Some Cauchy integral formulas of a holomorphic function on a closed ball in Cn are constructed and the Taylor series expansion is deduced.     

A THEOREM ON THE CONVERGENCE OF SUMS OF INDEPENDENT RANDOM VARIABLES

1 IntroductionThroughout this paperl {X., n 2 1} is assumed to be a sequence of independent randomvariables. Fn denotes the distribution function of the partial surns S. = Z Xk. As is known,k = 1oothe series Z X. is said to be essentially convergent (a.s.) if there exists a sequence of constantsn = 1oo{b., n 2 1} such that Z (X. -- 6.) a.s. converges. When this happens we writeClearlyFn(x) = G.(x -- B.). (l.2)Our problem stems from an old conjecture in Probabilistic Number Theory sugges…