连通域上的Toeplitz算子

复平面内单位圆周上的Hardy空间中具有连续符号的Toeplitz算子指标公式的证明依赖于Hopf定理,然而,Hopf定理在一般连通域上并不成立,因此,一般连通域上Toeplitz算子指标公式的证明需要不同于单位圆情形下的方法.本文就有限连通域的情形得到了具有连续符号的Toeplitz算子的指标公式.同时,还讨论了一般连通域上Toeplitz代数的上同调群.此外,还讨论了符号在QC中的Toeplitz算子.     

一般边界条件下Sturm-Liouville算子的Ambarzumyan型定理

该文研究有限区间上一般自伴边界条件下的Sturm-Liouville方程的逆特征值问题.将Neumann边界条件下Sturm-Liouville方程的Ambarzumyan型定理推广到一般自伴边界条件下情形,证明了如果它的特征值与零势的特征值一样,则Sturm-Liouville方程的势为零.     

次正常算子和亚正常算子的注记

对具有自交换子为有限秩的次正常算子,证明了Voiculescu的一个猜想成立。利用亚正常算子理论的技巧,得到了C(D)的一个稠密性定理。     

左定Sturm-Liouville算子的特征值计算(英文)

研究了定义在有限区间[a,b]上的具有分离型和混合型边界条件的左定正则Sturm-Liouville算子的特征值问题.把具有混合型边界条件的左定正则Sturm-Liouville问题转化成二维的、具有分离型边界条件的右定正则Sturm-Liouville问题,给出了具有混合型边界条件的左定正则Sturm-Liouville算子的特征值的数值计算方法.     

非archimedean Banach 空间上算子的值域包含定理

本文给出了几个关于一般赋值域上Banach 空间上的算子的值域包含定理. 这些定理说明: 算子的值域包含、算子的强弱以及算子的分解之间有着重要的联系. 我们发现, 这些结果强烈地依赖于空间的连续延拓性质. 在经典情况下, Hahn-Banach 定理保证了连续延拓性质自然满足; 然而, 在非 archimedean 范畴下, 这种性质可能并不满足. 我们还给出一些反例说明, 这些结果在某种意义下已经不能再改进了.     

一类无界算子的Weyl定理

研究了一类无界算子的Weyl定理,刻画了具有扰动的无界自伴算子的Weyl定理.     

解析算子函数空间上的复合算子理论初步

本文将经典Hardy空间上复合算子的理论、方法应用到解析算子函数空间上,给出了解析算子函数空间的几个基本性质及复合算子的有界性条件.     

区间数Heronian平均算子

定义了区间数Heronian平均算子以及区间数加权Heronian平均算子,并探讨了它们的性质.然后,提出了区间数几何Heronian平均算子以及区间数几何加权Heronian平均算子,并研究了它们的性质.最后,将区间数加权Heronian平均算子和区间数几何加权Heronian平均算子应用于多属性决策,说明了它们的有效性.     

随机单调算子的满射性及应用

研究Banach空间中的随机单调算子,建立了连续随机单调算子的随机锐角原理、随机满射定理、随机双射定理及Hilbert空间上的一类连续随机算子的新的随机不动点定理,并应用随机强单调算子理论讨论了随机Hammerstein积分方程随机解的存在唯一性.     

基于连续区间有序几何加权平均Power算子的区间型组合预测模型

在COWG算子和WPA算子的基础上,构建新的COWG-WPA算子,该算子可将区间数转换成实数,同时兼顾数据自身、数据位置、数据与数据彼此间三者的重要性。将COWG-WPA算子应用于区间型组合预测问题中,在广义绝对误差λ次和的准则下建立了基于连续区间有序几何加权平均Power算子的区间型组合预测模型,分析了该模型是非劣性组合预测、优性组合预测的充分条件定理。最后通过实证分析进行对比,结果显示所建立的模型能有效提高预测的精度。     

New convolutions and their applicability to integral equations of Wiener-Hopf plus Hankel type

We propose four new convolutions exhibiting convenient factorization properties associated with two finite interval integral transformations of Fourier-type together with their norm inequalities. Moreover, we study the solvability of a class of integral equations of Wiener-Hopf plus Hankel type (on finite intervals) with the help of the factorization identities of such convolutions. Fourier-type series are used to produce the solution formula of such equations, and a Shannon-type sampling formula is also obtained.     

Spectral analysis of diffusions with jump boundary

In this paper we consider one-dimensional diffusions with constant coefficients in a finite interval with jump boundary and a certain deterministic jump distribution. We use coupling methods in order to identify the spectral gap in the case of a large drift and prove that there is a threshold drift above which the bottom of the spectrum no longer depends on the drift. As a corollary to our result we are able to answer two questions concerning elliptic eigenvalue problems with non-local boundary conditions formulated previously by Iddo Ben-Ari and Ross Pinsky.     

Compact inverses of first-order normal differential operators

In this work, firstly we describe all normal extensions of a minimal operator generated by linear differential-operator expression of first order in the Hilbert space of vector functions in finite interval. Later on, we investigate discreteness of spectrum and asymptotical behavior of s-numbers of the inverses of these normal extensions.     

Operators Represented by Conditional Expectations and Random Measures

On standard measure spaces every order continuous linear map between two ideals of almost everywhere finite measurable functions can be represented by a random measure. An analogue of this theorem is proved for the case of arbitrary σ-finite measure spaces. This fact leads to a proof that every order continuous linear map between ideals of almost everywhere finite measurable functions on σ-finite measure spaces is multiplication conditional expectation representable. This sheds further light on the structure of order continuous operators. Mathematics Subject Classification (20000): 47B38, 47B65 J.J. Grobler-Financial assistance of the NRF is gratefully acknowledged. D.T. Rambane-Financial assistance of the University of Venda research fund is gratefully acknowledged.     

Inverse spectral problem for integro-differential operators

In this paper, we study the inverse spectral problem on a finite interval for the integro-differential operator ? which is the perturbation of the Sturm-Liouville operator by the Volterra integral operator. The potential q belongs to L ₂[0, π] and the kernel of the integral perturbation is integrable in its domain of definition. We obtain a local solution of the inverse reconstruction problem for the potential q, given the kernel of the integral perturbation, and prove the stability of this solution. For the spectral data we take the spectra of two operators given by the expression for ? and by two pairs of boundary conditions coinciding at one of the finite points.     

Shellability of Interval Orders

An finite interval order is a partially ordered set whose elements are in correspondence with a finite set of intervals in the line, with disjoint intervals being ordered by their relative position. We show that any such order is shellable in the sense that its (not necessarily pure) order complex is shellable.     

Uniquely orderable interval graphs

Interval graphs and interval orders are deeply linked. In fact, edges of an interval graphs represent the incomparability relation of an interval order, and in general, of different interval orders. The question about the conditions under which a given interval graph is associated to a unique interval order (up to duality) arises naturally. Fishburn provided a characterisation for uniquely orderable finite connected interval graphs. We show, by an entirely new proof, that the same characterisation holds also for infinite connected interval graphs. Using tools from reverse mathematics, we explain why the characterisation cannot be lifted from the finite to the infinite by compactness, as it often happens.     

Investigation of the spectral properties of a fourth order differential operator with finite transmission conditions

In this paper, the spectral analysis of a singular dissipative fourth order differential operator in lim‐4 case with finite transmission conditions is investigated. For this purpose, the inverse operator with explicit form is used. Finally, with the help of Liv?ic's theorem, it is proved that all root vectors of the fourth order dissipative operator in lim‐4 case with finite transmission conditions are complete in the Hilbert space. Copyright © 2015 John Wiley & Sons, Ltd.     

一类随机非自伴波方程的半离散有限元近似

本文研究了由白噪音驱动的随机非自伴波方程的有限元近似,由于线性算子A非自伴,不能应用A的特征值和特征向量,从而得到的结果更具有一般性.空间离散上采用标准的有限元法,并借助强连续算子函数的性质,得到了该方程的强收敛误差估计.本文方法也适用于多维情况的分析.最后用数值算例验证了理论分析的正确性.     

Unique solvability of pseudohyperbolic equations with singular right-hand sides

In this paper, we consider the solvability of the Cauchy problem for pseudohyperbolic equations (partial differential equations of third order). For the case in which the right-hand side is a generalized function (distribution) of finite order, we establish a theorem on the unique solvability for a sufficiently general pseudohyperbolic operator. The method of proof is based on a specially constructed “scale” of a priori inequalities for the direct and adjoint operators.