Stieltjes函数生成的广义Loewner矩阵的秩不变性

研究由Stieltjes函数生成的两类广义Loewner矩阵的秩不变性,证明了由同一Stieltjes函数生成的第一类同型的广义Loewner矩阵的秩是相等的,而生成的第二类同型的广义Loewner矩阵的秩相等或者相差1.     

某些Mercer核矩阵的权范数

借助整函数插值研究由函数的广义平移所生成的Mercer核矩阵及其逆矩阵权范数的上、下界估计问题,将定义在无限区间上整函数的广义平移所生成的Mercer核矩阵权范数界的估计转化为其Fourier-Bessel变换来估计.     

Pascal矩阵的一种显式分解

本文引入了两种广义Pascal矩阵凡,P_n,k,Q_n,k以及两种广义Pascal函数矩阵O_n,k[x,y],Q_n,k[x,y],证明了Pascal矩阵能够表示成(0,1)-Jordan矩阵的乘积而且Pascal函数矩阵能分解成双对角矩阵的乘积.     

Stirling数和Pascal矩阵函数

Call和Velleman(1993)引入了Pascal矩阵函数.Cheon和Kim(2001)应用Pascal矩阵函数分解第一类和第二类Stirling数.本文引入移位Stirling矩阵,并用Pascal矩阵对其分解.最后讨论引入广义Stirling数及其矩阵.He(2013)以及Hsu和Shiue(1998)对后者有一系列的讨论.本文中的矩阵等式反映了第一类、第二类和广义Stirling数以及二项式数之间的关系,而且形式简洁,有助于发现更多的性质.     

涉及正定矩阵的一些函数的凸性及其应用

利用张量积的性质以及关于矩阵酉不变范数的两个不等式,研究了涉及正定矩阵的几个映射及函数的凸性,通过所得结果得到了关于矩阵迹、积和式及广义矩阵函数的一些不等式,并给出其在量子信息论中的一些应用.     

矩阵值Caratheodory函数广义块Pick矩阵的秩不变性

Lasarow^[1]推导出矩阵值Carath\'{e}odory函数的第一、第二型广义块Pick矩阵及其变型的秩不变性. 这些矩阵由同一个Carath\'{e}odory函数的值与它的直到某阶的导数值确定. 利用文献[2]中提出的块Toeplitz向量方法, 该文断言,这些块矩阵的秩分别相关并重合于具有秩不变性的块Toeplitz矩阵的秩, 从而改进了这两类广义块Pick矩阵的秩不变性结论的证明.     

一个二元矩阵插值连分式的展开式

本文借助于文[1]定义的一种实用的矩阵广义逆,构造了一个二元Stieltjes型矩阵值插值连分式的展开式,它的截断分式可以定义二元矩阵值插值函数.     

线性微分系统的广义反射函数

研究了线性微分系统的广义反射函数,作为应用,给出了线性微分系统具有三角型反射矩阵的充要条件.     

广义系统正则状态观测器的存在性和设计

水文借助于广义函数与矩阵广义逆理论,在前人工作的基础上证明了广义系统的(包括干扰解耦的)正则状态观测器的设计问题,等价于一个低于rank E阶的正则系统的相应问题,从理论上解决了广义系统正则状态观测器的设计问题。     

一四元数矩阵方程组的最佳逼近解

利用四元数矩阵的广义Frobenius范数和弱圈积,建立一个关于四元数矩阵的实函数并简洁表征其极小值.再用四元数矩阵的奇异值分解和广义Frobenius范数的性质,讨论四元数矩阵方程组[AX,XB]=[C,D]的最小二乘解,得到了解的具体表达式.最后在该方程组的解集合中导出了与给定矩阵的最佳逼近解的表达式.     

Generalized cardinal B-splines: Stability, linear independence, and appropriate scaling matrices

Generalized cardinal B-splines are defined as convolution products of characteristic functions of self-affine lattice tiles with respect to a given integer scaling matrix. By construction, these generalized splines are refinable functions with respect to the scaling matrix and therefore they can be used to define a multiresolution analysis and to construct a wavelet basis. In this paper, we study the stability and linear independence properties of the integer translates of these generalized spline functions. Moreover, we give a characterization of the scaling matrices to which the construction of the generalized spline functions can be applied.     

Applications of spherical functions in multilinear algebra

Spherical functions are shown to organize and unify previous work on generalized matrix functions and symmetry classes of tensors. At the same time, new areas of investigation are suggested.     

A method for determining the partial indices of symmetric matrix functions

We propose a method for determining the partial indices of matrix functions with some symmetries. It rests on the canonical factorization criteria of the author’s previous articles. We show that the method is efficient for the symmetric classes of matrix functions: unitary, hermitian, orthogonal, circular, symmetric, and others. We apply one of our results on the partial indices of Hermitian matrix functions and find effective well-posedness conditions for a generalized scalar Riemann problem (the Markushevich problem).     

Remark to an unambiguity of estimators in the universal linear statistical models with the type ii constraints

In the universal linear statistical model with the type II constraints, estimates of the unbiasedly estimable linear functions of the parameters of the mean value vector are given by special types of generalized matrix inverse. Since there exists many versions of such matrix inverse it is of some interest to check the unambiguity of obtained estimators. The aim of the paper is to find the best unbiased linear estimators of unbiasedly estimable functions and to show that they do not depend on the choice of the used generalized inverse of the matrices.     

On rank variation of block matrices generated by Nevanlinna matrix functions

Within the framework of the multiple Nevanlinna–Pick matrix interpolation and its related matrix moment problem, we study the rank of block moment matrices of various kinds, generalized block Pick matrices and generalized block Loewner matrices, as well as their Potapov modifications, generated by Nevanlinna matrix functions, and derive statements either on rank (or inertia) invariance in different senses or on rank variation of such types of block matrices (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The construction of wavelets from generalized conjugate mirror filters in

The classical constructions of wavelets and scaling functions from conjugate mirror filters are extended to settings that lack multiresolution analyses. Using analogues of the classical filter conditions, generalized mirror filters are defined in the context of a generalized notion of multiresolution analysis. Scaling functions are constructed from these filters using an infinite matrix product. From these scaling functions, non-MRA wavelets are built, including one whose Fourier transform is infinitely differentiable on an arbitrarily large interval.     

Approximation of functions from L p (ω) β by matrix means of their Fourier series

We formulate some special conditions for the integrable functions and moduli of continuity. We give the results on rate of approximation of such functions by matrix means of their Fourier series, where the entries of the rows of the matrix generate the sequences belonging to the classes MRBVS and MHBVS, We also present some results on norm approximation for functions from the generalized integral Lipschitz classes.     

Generalized canonical factorization of matrix and operator functions with definite hermitian part

It is proved that rational matrix functions with definite hermitian part on the real line admit a generalized canonical factorization. The functions are allowed to have poles on the real line. A generalization of this result to a class of operator functions is obtained as well.Partially supported by an NSF grant     

Special matrix functions: characteristics,achievements and future directions

ABSTRACT

In recent years, special matrix functions and polynomials of a real or complex variable have been in a focus of increasing attention leading to new and interesting problems. In this work, we present matrix space analogues to generalized some functions and polynomials in the framework of matrix setting. Many of the special matrix functions and polynomials are constructed along standard procedures. Recently published papers are also surveyed and we list the most essential ones.     

On the hypergeometric matrix functions of two variables

We introduce the generalized hypergeometric function with matrix parameters. We also define two variable Appell matrix functions and find their regions of convergence as well as integral representations.