非线性非单调二元算子方程组的解及其应用

利用非线性泛函分析中的锥理论和单调迭代的方法,研究了一类非线性非单调二元算子方程组的解的存在性,并给出了收敛于解的迭代序列,然后作为应用,得到了B anach空间中的一类非线性V olterra型积分方程组的解,改进了最近的许多结果.     

泛函分析若干基本概念的理解

本文结合工程问题对线性算子、算子的三种收敛性等泛函分析中若干基本概念进行了直观化的理解,分别阐述了共轭算子在经济学中的含义及相伴算子在力学中的含义,通过将泛函分析中的基本概念还原到具体学科中加深了对概念的理解.     

连续小波变换及小波框架算子的一些性质

以泛函分析的观点来考察连续小波变换及小波框架算子，得到了它们的一些性质，并给出了严格证明，弥补了有关献中的不足。     

λ-Kantorovich算子的逼近性质

首先在无穷空间上构造了一类新的λ-Szász-Kantorovich算子,通过分析计算得到了该类算子矩的估计及Korovkin型逼近性质;其次,利用连续模和K-泛函的等价关系给出了收敛速度的刻画;最后,借助于Holder不等式建立了Lipschitz连续函数的收敛定理.     

随机赋范空间算子随机范数与Hahn-Banach延拓定理

基于概率测度理论基础,研究了随机赋范空间中算子随机范数,得到了线性算子空间与线性泛函的若干随机化结果与随机化的Hahn-Banach延拓定理.结果可能成为随机泛函分析与概率论及应用的理论工具.     

再生核空间中的微分算子样条小波

0　引　　言r次多项式样条小波是从一个满足特殊的广义微分方程Dr+1φ(x)=δ(x)(D是广义微分子算子)的解φ(x)=xr+r!出发来构造的,文献[1]根据这一思想给出非多项式的H1(R)空间中微分算子样条小波分析的构造方法,本文基于这一思路来讨论W2(R)空间中的微分算子样条小波理论.在W2(R)空间中讨论非多项式形式的微分算子样条小波分析理论,这是多项式小波理论自然深入的发展.本文首先给出W2(R)空间中小波分析定义,然后给出小波函数在时、频域上的表达式,最后利用W2(R)空间中的若干特殊性质,给出小波的投影表达式.并证明了投影逼近函数uj(X)…     

Banach空间中极大单调算子零点的迭代构造

设E为实光滑、一致凸Banach空间,E*为其对偶空间,TE×E*为极大单调算子且T-10≠φ.本文引入了一种新迭代格式,利用Lyapunov泛函和广义投影算子等技巧,在Banach空间中证明了迭代序列弱收敛于极大单调算子T的零点的结论.     

小波分析中的一个非线性算子

在这篇文章里,我们以算子的观点考虑了小波的构造问题．结果,我们得到了小波分析中一个非线性算子并调查了这个非线性算子的一些性质．     

寿命为爱尔兰分布的可修闭路排队模型时间依赖解的渐近性质

利用C_0-半群理论研究寿命为爱尔兰分布的可修闭路排队系统.首先利用泛函分析中的Hille-Yosida定理,Phillips定理和Fattorini定理证明此排队系统模型正时间依赖解的存在唯一性.然后通过研究该模型相应主算子的谱的特征,分别得到虚轴上除了0外其他所有点都属于该模型主算子的豫解集与0是其主算子及其共轭算子的几何重数为1的特征值.最后将上述结果结合在一起推出该模型的时间依赖解强收敛于其稳态解.     

Banach空间中极大单调算子零点的带误差项的新迭代格式

令E为实光滑、一致凸Banach空间,E为其对偶空间,AE×E为极大单调算子且A-10≠Φ.本文将引入新的迭代算法,并利用Lyapunov泛函,Qr算子与广义投影算子等技巧,证明了迭代序列弱收敛于极大单调算子A的零点的结论.     

Circulant Wavelet Preconditioners for Solving Elliptic Differential Equations and Boundary Integral Equations

In this paper is discussed solving an elliptic equation and a boundary integral equation of the second kind by representation of compactly supported wavelets. By using wavelet bases and the Galerkin method for these equations, we obtain a stiff sparse matrix that can be ill-conditioned. Therefore, we have to introduce an operator which maps every sparse matrix to a circulant sparse matrix. This class of circulant matrices is a class of preconditioners in a Banach space. Based on having some properties in the spectral theory for this class of matrices, we conclude that the circulant matrices are a good class of preconditioners for solving these equations. We called them circulant wavelet preconditioners (CWP). Therefore, a class of algorithms is introduced for rapid numerical application.     

时频分析与算子代数

Gabor分析中几个著名的基本定理(如对偶原理和稠密性定理)与群表示和算子代数理论密切相连.尽管时频分析与算子代数之间的某些联系是Jon von Neumann于1930年代建立的,可是它们在近期得到广泛研究,这主要应归于小波/Gabor理论或更一般的框架理论近二十年的发展.本文将讨论过去几年得到的一些主要结果,同时也给出一些新的结果、解释和问题,我们主要考虑来源于时频分析并能反映与群表示理论存在内在联系的那些结果.特别地,针对群表示的时频分析,将详细说明抽象的对偶原理及其与算子代数理论中几个公开问题的联系.     

An infinite family of p-adic non-Haar wavelet bases and pseudo-differential operators

In this paper an infinite family of new compactly supported non-Haar p-adic wavelet bases in is constructed. We also study the connections between wavelet analysis and spectral analysis of p-adic pseudo-differential operators. A criterion for a multidimensional p-adic wavelet to be an eigenfunction for a pseudo-differential operator is derived. We prove that these wavelets are eigenfunctions of the fractional operator. Since many p-adic models use pseudo-differential operators (fractional operator), these results can be intensively used in these models. The text was submitted by the authors in English.     

Algebraic Properties of Subdivision Operators with Matrix Mask and Their Applications

Subdivision operators play an important role in wavelet analysis. This paper studies the algebraic properties of subdivision operators with matrix mask, especially their action on polynomial sequences and on some of their invariant subspaces. As an application, we characterize, under a mild condition, the approximation order provided by refinable vectors in terms of the eigenvalues and eigenvectors of polynomial sequences of the associated subdivision operator. Moreover, some necessary conditions, in terms of nondegeneracy and simplicity of eigenvalues of a matrix related to the subdivision operator for the refinable vector to be smooth are given. The main results are new even in the scalar case     

Wiener-Hopf equation: Kernels representable as a superposition of complex-valued exponents

The paper studies the Wiener-Hopf equations with kernels representable as superposition of complex-valued exponents. Such kernels arise in the kinetic gas theory, in the radiation transfer, etc. By application of a special, three-factor expansion of the initial uninvertible operator, the solution of the considered equation is reduced to those of two simple Volterra equations and a Wiener-Hopf integral equation with a contractive operator. A structural existence theorem is proved.     

A new class of operators and a description of adjoints of composition operators

Starting with a general formula, precise but difficult to use, for the adjoint of a composition operator on a functional Hilbert space, we compute an explicit formula on the classical Hardy Hilbert space for the adjoint of a composition operator with rational symbol. To provide a foundation for this formula, we study an extension to the definitions of composition, weighted composition, and Toeplitz operators to include symbols that are multiple-valued functions. These definitions can be made on any Banach space of analytic functions on a plane domain, but in this work, our attention is focused on the basic properties needed for the application to operators on the standard Hardy and Bergman Hilbert spaces on the unit disk.     

H∞和Bergman空间之间的加权复合算子

本文研究H∞和Bergman空间之间加权复合算子uCφ的有界性或紧性,利用泛函分析及复分析的方法,获得了uCφ是有界算子或紧算子的充要条件在H∞和Bergman空间之间的范数估计,推广了各类解析函数空间上加权复合算子的相应理论.