Characteristic Conditions for the Generation of α-Times Resolvent Families on a Hilbert Space

In 2000,Shi and Feng gave the characteristic conditions for the generation of C0semigroups on a Hilbert space.In this paper,we will extend them to the generation of α-times resolvent operator families.Such characteristic conditions can be applied to show rank-1 perturbation theorem and relatively-bounded perturbation theorem for α-times resolvent operator families.     

具有内部构造安全保障体系的冗余机器系统的特征值的问题

对具有内部构造安全保障体系的冗余机器系统中的特征值的存在性进行了分析求解,给出了实例,并对该系统的特征值进行了一个特征值对应一个特征向量的求征.     

具有四个状态可修复系统本征值分布

给出一类具有四个状态可修复系统算子预解式特性,对任意给定的δ>0,r=a+bi,固定a1,a2,使得-μ+δ相似文献   

Hilbert空间上$\alpha$-次预解算子族的生成元特征

In 2000,Shi and Feng gave the characteristic conditions for the generation of C0semigroups on a Hilbert space.In this paper,we will extend them to the generation of α-times resolvent operator families.Such characteristic conditions can be applied to show rank-1 perturbation theorem and relatively-bounded perturbation theorem for α-times resolvent operator families.     

两不同部件并联可修系统的本征值分布

给出两不同部件并联可修系统算子预解式特性,对任意给定的δ>0,r=a+bi,固定a1,a2(-μ+δ相似文献   

具有早期储备可修复收入系统的谱分析

研究了具有早期储备可修复系统,首先给出了该系统的预解式,对δ>0,γ=a+bi,固定a1,a2,满足-μ+δ相似文献   

具有易损坏储备部件可修系统谱的特性

研究了R(r;A+E)的性质,给出了修复系统预解式的特性.对任意给定的δ>0,r=a+bi,-μ+δ相似文献   

一类人与出租车构成的排队模型主算子的谱特征

运用C0-半群理论研究一类人与出租车构成的排队模型主算子的谱特征.首先证明0是对应于该排队模型的主算子的几何重数为1的特征值,其次证明在虚轴上除了0以外其他所有点都属于该算子的豫解集,然后证明0是该主算子共轭算子的特征值.     

ASYMPTOTIC FORMULAE OF EIGENVALUE-COUNTING FUNCTION FOR ELLIPTIC EIGENVALUE PROBLEMS ON A BOUNDED DOMAIN WITH A FRACTAL BOUNDARY

IIntroductlonLet fi be a bounded open set In the n－dimensional Euclldean space R”withtheboundaryo0．In this paper,we shallessentiallydeal with thefollowingeigenvalue problem:,nD 一)。o…4km)螂川川J”人川川,x〔u,丸 人k＝1\“’“)llillj＝U．U b UI[。where丸 meanso/axj,and we suPPose that coeaclents aj。(x),J;k＝ 1,2;…,。satisfy the following conditions:(1)aj。(x)is real function and belong to Cm(R”);(2)There exists an M＞0;such that Iajk(x)l＜M;;;k二 1,2,…,n;148 Ann ofDiff Eqs Vol…     

具有内部构造安全保障体系的冗余机器系统的特征值分布

给出了具有内部构造安全保障体系的冗余机器系统算子预解式特性,对任意给定的δ>0,r=a+bi,固定a1,a2,使得(-μ+δ相似文献   

Generalized Mixed Variational Inequalities and Resolvent Equations

In this paper, we introduce and study a new class of variational inequalities, which is called the generalized mixed variational inequality. Using essentially the resolvent operator concept, we establish the equivalence between the generalized mixed variational inequalities and the system of resolvent equations. This equivalence is used to suggest a number of new iterative algorithms for solving the variational inequalities. Several special cases are discussed which can be obtained from the main results of this paper.     

On some notions of convergence for n‐tuples of operators

The aim of this paper is to show that we can extend the notion of convergence in the norm‐resolvent sense to the case of several unbounded noncommuting operators (and to quaternionic operators as a particular case) using the notion of S‐resolvent operator. With this notion, we can define bounded functions of unbounded operators using the S‐functional calculus for n‐tuples of noncommuting operators. The same notion can be extended to the case of the F‐resolvent operator, which is the basis of the F‐functional calculus, a monogenic functional calculus for n‐tuples of commuting operators. We also prove some properties of the F‐functional calculus, which are of independent interest. Copyright © 2013 John Wiley & Sons, Ltd.     

Extension of Transient Resolvents

For a submarkovian resolvent U=(U )_>0 with bounded initial kernel U ₀ on a Radon space X, we construct a minstable cone of potentials C on a compact metrizable space YX such that U extends to a subordonated (to C) resolvent on Y.     

On Some Results Concerning the Reduite and Balayage

If J is an analytic, saturated gambling house with compact sections, and we show that there exists a (submarkovian) borel kernel P permitted in J such that μ = λP. If is a proper submarkovian resolvent on a Lusin space X, we study the regularity of the reduite R^A_s of an excesive function s on a set A ⊂ X.     

Some singular third-order boundary value problems

In this paper, we consider some singular formally symmetric (self-adjoint) boundary value problems generated by a singular third-order differential expression and separated and coupled boundary conditions. In particular, we consider that the minimal symmetric operator generated by the third-order differential expression has the deficiency indices (3,3). We investigate same spectral properties related with these problems, and we introduce a method to find the resolvent operator.     

Robust Bounds for Krylov Methods

In this paper we give bounds for polynomials of operators. These bounds are robust in low rank perturbations. This problem is encountered in the study of the convergence of Krylov methods. The central idea here is to view the resolvent as a meromorphic function.     

A new identity for resolvents of matrices

A new identity for resolvents of matrices is suggested. We show that in appropriate situations, it is more convenient than the Hilbert identity. In particular, we establish new invertibility conditions for perturbed matrices as well as new bounds for the spectrum of perturbed matrices.     

Hilbert空间上依范连续的α-次预解算子族

主要运用Laplace-Stieltjes的方法,讨论Hilbert空间上α-次预解算子族的依范连续性与其预解式的关系,得到一个主要结果：Hilbert空间上α-次预解算子族的依范连续性与其预解式在当｜τ｜→∞时,‖（ω＋iτ）~（α-1）R（（ω＋iτ）~α,A）‖→0等价.     

L~P（Ω）空间余弦算子函数的谱特征

本文得到Ｌ￣Ｐ（Ω）（１＜ｐ＜∞）空间余弦算子函数，用生成元性质表示的谱特征。     

Resolvent bounds for jump generators

The paper deals with jump generators with a convolution kernel. Assuming that the kernel decays either exponentially or polynomially, we prove a number of lower and upper bounds for the resolvent of such operators. In particular we focus on sharp estimates of the resolvent kernel for small values of the spectral parameter. We consider two applications of these results. First we obtain pointwise estimates for principal eigenfunction of jump generators perturbed by a compactly supported potential (so-called nonlocal Schrödinger operators). Then we consider the Cauchy problem for the corresponding inhomogeneous evolution equations and study the behaviour of its solutions.