自伴算子

并将任一自伴算子表示成某一算子值函数的σ-弱积分。

We represent a self-adjoint operator as the σ - weak integral of an operator-valued function .

类似与标型谱算子，U-标算子是否拟仿射相似于自伴算子是一“公开问题”。

Whether a U-scalar operator is a quasi-affine transform of a self-adjoint operator , similar to a spectral operator of scalar type , is an open question .

自伴算子的Jordan代数上的双Jordan导子

Bi-Jordan Derivations on Jordan Algebras of Selfadjoint Operators

该文给出了它的另一种证明，同时应用算子分解和函数演算，证明了复Hilbert空间上的自伴算子的几个重要范数不等式。

By spectral decomposition of a Hermitian operator and functional calculus , some important norm inequalities on complex Hilbert space are obtained .

研究了一类变系数自伴算子&Heisenberg群上的Kohn－Laplace算子多项式的特征值问题.利用Heisenberg群上的表示及其Fourier变换，获得了该特征值问题的特征值的一些先验估计。

The work is devoted to eigenvalue problems associated with a class of variable coefficients selfadjoint operators & Kohn Laplace operator on Heisenberg group . One obtains some priori estimate for discrete eigenvalues of the problem by group representation and Fourier transformation theory on n dimensional Heisenberg group .

利用Lyapunov-Perron方法在适当的谱间隙条件和适当小的时滞假设下，证明了一类非自伴算子情形下半线性时滞抛物方程惯性流形的存在性。

The present paper deals with the long time behavior of semilinear parabolic equations with time delays in the non-self adjoint case . Under the condition of right spectral gap and the assumption of properly small delay time , the existence of inertial manifolds is proved by Lyapunov-Perron method .

非自伴算子问题的自伴变分表述

The Self-adjoint Variational Formulation of Problems Having Non-Self-adjoint Operators

非自伴算子代数的换位子

Commutators of Non-Self-Adjoint Operator Algebras

算子代数的研究始于二十世纪三十年代，而非自伴算子代数是算子代数理论的重要分支。

The study of operator algebra theory began in 1930 ' s.Non-selfadjoint operator algebra is an important branch of theory of operator algebra .

利用伴随算子和伴随场函数，建立了低频涡流电磁场中非自伴算子问题的一般变分描述。

A system procedure is proposed to derive the variational principle for a non self adjoint low frequency eddy current problem through adjoint operator and adjoint function .

本文利用线性算子的谱理论给出了逻辑序下两个自伴算子下确界的谱表示。

In this note , using the spectral theory of linear operators , a spectral representation of infimum of two self-adjoint operators with respect to the logic order is established .

一个非自伴Dirac算子的特征展开

The eigenvalue expansion of a non-self-adjoint Dirac operator

从所得结果来看，对于非自伴Dirac算子来说，特征展开问题具有相当丰富的内容。

For the non-self-adjoint Dirac operators , there are plentiful content in the problems of eigenvalue expansion problems .

在一般线性两点边值条件下生成自伴Dirac算子的条件被证明了。

The condition under which the Dirac operator is self-adjoint is discussed under the general linear boundary condition between the interval of two points .

高阶J-自伴微分算子的豫解算子

The Resolvent Operators of High Order J Selfadjoint Differential Operators

一条摄动定理及其对非自伴微分算子广义本征展开的应用

A Perturbation Theorem and Its Applications to the Generalized Eigenfunction Expansions of Some Non-Self-Adjoint Differential Operators

考虑一类微分算式中具有对数函数系数的自伴微分算子，并主要通过构造奇异序列的方法得到了一定条件下算子的本质谱。

We considered a class of self-adjoint differential operators with logarithmic coefficients in the expressions , and got the essential spectrum of the operators under certain conditions by constructing singular sequences .

常系数J-自伴Euler微分算子的本质谱

The Essential Spectrum of Euler Differential Operators with Constant Complex Coefficients

Hilbert空间有界自伴正可逆算子的一个不等式

An inequality on the positive definite operator in Hilbert space

2n阶J-自伴向量微分算子的预解算子及其谱

The Resolvent Operator and Spectrum of 2n-order J-self-adjoint Vector Differential Operator

并在此Hilbert空间中，定义了一个包含声辐射性质并且是线性自伴正的算子。

And in the Hilbert space , an operator is defined , which includes the radiation property of the vibrating surface and is linear , self-adjoint and positive .

研究具反射边界条件，非自伴非紧算子的抽象边界问题，证明了它等价一个Wiener-Hopf方程，并证明了方程的适定性。

In this paper , the abstract boundary value problem of non-selfadjoint and non-compact operator with reflective boundary condition is studied . It is obtained that the this kind of problems is equal to a Wiener-Hopf equation and the well poset problem of the abstract boundary value is proved .

自伴椭圆型微分算子伴有边界摄动非线性积分微分方程系统的奇摄动

Singular Perturbation for System of Nonlinear Integral Differential Equations with Boundary Perturbation

第四章研究了二阶自伴向量微分算子，得到其谱是离散的两个充分条件。

Two sufficient conditions for the discreteness of two-order self-adjoint vector differential operator are given in last part .

直和空间上极限圆情形的自伴Sturm－Liouville算子的谱分解

Spectral Decomposition of Self-Adjoint Sturm-Liouville Operator in Limiting Circle Case in Direct Sum Spaces