关于算子组Taylor谱的定义

给出了关于算子组Taylor谱的另一种定义及ε-联合伪谱的定义,并讨论了它的一些性质以及关于交叉交换算子组在这几种定义下的一些结果．     

联合半亚正常算子组的Taylor联合谱

本文定义了非重交换的联合半亚正常算子组,证明了谱分割定理和谱投影定理,提示了半亚正常算子组的 Taylor 联合谱与它们的记号算子组的 Taylor 联合谱之间的关系.     

投影算子组的联合谱

本文研究Hilbert空间H上投影算子组的联合谱.首先通过计算给出正则投影对的联合谱,进而给出一般的投影算子对的联合谱.本文还对两个投影算子的和与差的可逆性给出一些等价刻画.特别地,当P和Q为正则投影对时,本文通过计算算子组[I, P, Q]的联合谱来给出σ(P+Q)和σ(P-Q)的具体刻画.反过来,本文证明两类具有特定形式的复数集分别是Hilbert空间上正则投影对的和与差的谱.本文也给出一般的投影算子对的和与差的谱.最后,本文计算特定条件下的3个投影算子组[P, Q, R]的联合谱.     

对角无穷维Hamilton算子点谱关于实轴的对称性

在不同条件下得到对角无穷维Hamilton算子点谱的两个组成部分σp（A）与σp（-A^＊）关于实轴对称的充分必要条件.以此为基础,完全刻画了对角无穷维Hamilton算子点谱关于实轴的对称性.     

上三角无穷维Hamilton算子的剩余谱

将点谱划分为四个部分,得到上三角无穷维Hamilton算子的点谱σ_p(H)关于虚轴对称的充要条件.在此基础上,结合无穷维Hamilton算子的谱结构,得到无穷维Hamilton算子剩余谱的完全描述,从而实现了利用其内部算子刻画剩余谱.     

关于算子谱的定义

本文给出了两个关于算子的算子谱的定义,并讨论了它的一些性质。这种定义,使算子谱的概念更接近于原来谱的概念。     

一类乘积算子点谱的对称性及其应用

证明了一类乘积算子点谱的对称性并将其应用到Hamilton算子、反Hamilton算子上,最后举例说明了乘积算子数值域的一些性质.     

NN算子及Weyl型定理

本文定义一种新的算子――NN算子,通过这种新算子定义的NN谱给出有界线性算子满足Weyl定理、a-Weyl定理、Browder定理和a-Browder定理的充要条件.     

周期边界条件下四阶特征值问题的一种有效的Fourier谱逼近

文章提出了周期边界条件下四阶特征值问题的一种有效的Fourier谱逼近方法.首先,根据周期边界条件引入了适当的Sobolev空间和相应的逼近空间,建立了原问题的一种弱形式及其离散格式,并推导了等价的算子形式.其次,定义了正交投影算子,并证明了其逼近性质,结合紧算子的谱理论证明了逼近特征值的误差估计.另外,构造了逼近空间中的一组基函数,推导了离散格式基于张量积的矩阵形式.最后,文章给出了一些数值算例,数值结果表明其算法是有效的和谱精度的.     

非线性Lipschitz连续算子的定量性质（Ⅳ）──谱理论

本文将有界线性算子谱的定义及若干重要谱性质推广至非线性Ｌｉｐｓｃｈｉｔｚ连续算子，并得到一些有意义的结果．     

Estimation of the measure of the image of the ball

Under study is the class of ring Q-homeomorphisms with respect to the p-module. We establish a criterion for a function to belong to the class and solve a problem that stems from M. A. Lavrentiev [1] on the estimation of the measure of the image of the ball under these mappings. We also address the asymptotic behavior of these mappings at a point.     

On the distributions of the ratios of the extreme roots to the trace of the Wishart matrix

In this paper, the authors cosider the derivation of the exact distributions of the ratios of the extreme roots to the trace of the Wishart matrix. Also, exact percentage points of these distributions are given and their applications are discussed.     

On the rational approximation of the sum of the reciprocals of the Fermat numbers

Let $\mathcal{G}(z):=\sum_{n\geqslant0} z^{2^{n}}(1-z^{2^{n}})^{-1}$ denote the generating function of the ruler function, and $\mathcal {F}(z):=\sum_{n\geqslant} z^{2^{n}}(1+z^{2^{n}})^{-1}$ ; note that the special value $\mathcal{F}(1/2)$ is the sum of the reciprocals of the Fermat numbers $F_{n}:=2^{2^{n}}+1$ . The functions $\mathcal{F}(z)$ and $\mathcal{G}(z)$ as well as their special values have been studied by Mahler, Golomb, Schwarz, and Duverney; it is known that the numbers $\mathcal {F}(\alpha)$ and $\mathcal{G}(\alpha)$ are transcendental for all algebraic numbers α which satisfy 0<α<1. For a sequence u, denote the Hankel matrix $H_{n}^{p}(\mathbf {u}):=(u({p+i+j-2}))_{1\leqslant i,j\leqslant n}$ . Let α be a real number. The irrationality exponent μ(α) is defined as the supremum of the set of real numbers μ such that the inequality |α?p/q|<q ^?μ has infinitely many solutions (p,q)∈?×?. In this paper, we first prove that the determinants of $H_{n}^{1}(\mathbf {g})$ and $H_{n}^{1}(\mathbf{f})$ are nonzero for every n?1. We then use this result to prove that for b?2 the irrationality exponents $\mu(\mathcal{F}(1/b))$ and $\mu(\mathcal{G}(1/b))$ are equal to 2; in particular, the irrationality exponent of the sum of the reciprocals of the Fermat numbers is 2.     

Refinement of the asymptotics of the power of the quantile test

One investigates the asymptotic properties of the quantile test, similar to the properties of the Pearson's chi-square test of fit.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 153, pp. 5–15, 1986.The author is grateful to D. M. Chibisov for useful remarks.     

On the approximation of positive operators and the behaviour of the spectra of the approximants

LetT be a positive linear operator on the Banach latticeE and let (S _n ) be a sequence of bounded linear operators onE which converge strongly toT. Our main results are concerned with the question under which additional assumptions onS _n andT the peripheral spectra (S _n ) ofS _n converge to the peripheral spectrum (T) ofT. We are able to treat even the more general case of discretely convergent sequences of operators.