非自伴算子代数的换位子

设T是复数域上的代数,T的换位子[T,T]指{[a,b]:a,6∈T}的线性扩张．本文给出了Nest代数T(N)的换位子[T(N),T(N)1]的σ-弱算子拓扑闭包的刻画,和TAF代数T的换位子[T,T]的范数闭包的几种刻画,进一步得到是T的理想．     

算子的算子点谱的判定

本文讨论了算子A∈B(H)     

算子的算子点谱的判定

本文讨论了算子Ａ∈Ｂ（Ｈ）_Ｎ为算子Ｔ∈Ｂ（Ｈ）的算子点谱的判定条件,特别得到：当Ｔ为亚正常算子时,Ａ为Ｔ的算子点谱的判定条件,另外还得到ｋｅｒτ^ｎ_Ｔ,Ａ＝ｋｅｒτ_Ｔ,Ａ成立的充分条件     

On the Spectrum of Degenerate Operator Equations

We study the distribution in the complex plane of the spectrum of the operator , generated by the closure in of the operation originally defined on smooth functions with values in a Hilbert space satisfying the Dirichlet conditions . Here and A is a model operator acting in . Criterial conditions on the parameter for the eigenfunctions of the operator to form a complete and minimal system as well as a Riesz basis in the Hilbert space H are given.     

Spectral Analysis of a Class of Non-Self-Adjoint Differential Operator Pencils with a Generalized Function

We investigate the spectrum and solve the inverse problem for a pencil of non-self-adjoint second-order differential operators with a generalized function in the space L₂(−∞, +∞). __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 145, No. 1, pp. 102–107, October, 2005.     

一类可靠性模型的主算子的谱

研究一个可靠机器,一个具有无穷容量的缓冲库和一个不可靠机器构成的系统的主算子的谱.当机器1的加工率λ,机器2的加工率μ,部件从机器1成功地传送到机器2的概率η₁,机器2成功处理完部件的概率η₂满足一定的条件时,证明-μ不是该系统的主算子的特征值.     

On the Absolutely Continuous Spectrum of Dirac Operator

Abstract

We prove that the massless Dirac operator in ?³ with long-range potential has an a.c. spectrum which fills the whole real line. The Dirac operators with matrix-valued potentials are considered as well.     

C－余弦算子函数的谱

Let A be the generator of a C-cosine operator functions C(t) on a Banach space X .The spectrum characterization of (unbounded) cosine operator function C(t)C^-1 on R(C²) is derived. In particular， we characterize the spectrum of strongly continuous cosine operator on a Banach space.     

On the Spectrum of the Weighted p-Biharmonic Operator with Weight

In this work we give a non decreasing sequence of positive eigenvalues of the weighted p-biharmonic operator with weight and with Navier boundary conditions, then we study the simplicity and the isolation of the first positive eigenvalue. Finally, we study the one dimensional case.     

On the Spectrum of the Reflection Operator on Conical Surfaces

We study the mapping properties of the reflection operator on a conical surface. This allows us to derive regularity results for the solution of the radiosity equation on conical surfaces in a scale of weighted Sobolev spaces. To motivate the calculations we first study the operator on a cylinder. Here we estimate the asymptotic behavior of the spectrum of the reflection operator by partial integration. This method works also for the conical case, but first we have to find a simple representation for some hypergeometric functions.     

On the Spectrum of an Equivariant Extension of the Laplace Operator in a Ball

We study the relationship between the well-posedness of an equivariant problem for the Poisson equation in a ball and the spectrum of the operator generated by it.     

Spectrum of a Model Operator in the Perturbation Theory of the Essential Spectrum

We consider a model operator acting in a subspace of a Fock space and obtain a symmetrized analogue of the Faddeev equation. For the operator considered, we describe the position and the structure of its essential spectrum.__________Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 144, No. 3, pp. 544–554, September, 2005.     

On Absolute Continuity of the Spectrum of a 3D Periodic Magnetic Dirac Operator

Absolute continuity of the spectrum of a 3D periodic magnetic Dirac operator is proved provided that the magnetic potential A belongs to the space \({H^q_{\mathrm{loc}},q >1 }\) , and the matrix potential \({\widehat V\in L^3_{\mathrm {loc}}}\) is represented in the form \({\widehat V=\widehat V_0+\widehat V_1}\) , where \({\widehat V_0}\) commutes and \({\widehat V_1}\) anticommutes with the Dirac matrices \({\widehat \alpha _j, j = 1, 2, 3}\) .     

On the Finiteness of the Discrete Spectrum of a Four-Particle Lattice Schrödinger Operator

A Hamiltonian describing four bosons that move on a lattice and interact by means of pair zero-range attractive potentials is considered. A stronger version of the Hunziker–Van Vinter–Zhislin theorem on the essential spectrum is established. It is proved that the set of eigenvalues lying to the left of the essential spectrum is finite for any interaction energy of two bosons and is empty if this energy is sufficiently small.     

On the Spectrum of Two-Point Boundary Value Problems for the Dirac Operator

Differential Equations - We consider the spectral problem for a Dirac operator with arbitrary two-point boundary conditions and an arbitrary complex-valued integrable potential. The existence of...