在本文中，我们研究了(ac)算子，可分解算子，谱算子以及它们之间的关系。
In this paper we investigated (AC) operators, decomposable operators, spectral operators and their relationships.
在第二章中，作者以谱分解、函数演算等为工具，给出一些重要的算子不等式与范数不等式。
In this chapter, we give some operator inequalities and norm inequalities by means of spectral decomposition and functional calculus.
摘要通过对积分算子谱的估计，作者给出了一阶线性微分差分方程在边值条件下解的存在唯一性定理。
In this paper, by estimates of spectral of an integral operator, the authors give a theorem on the existence of solutions for first order differential difference equations with boundary condition.
对一些整谱图，运用一种全新的广义线图算子方法，构造出了一系列无穷多个新的整谱图。
By using the operator generalized line graphs on some integral graphs, a series of infinite integral graphs is constructed.
谱论是泛函分析的一个近代重要分支，由矩阵特征值构思出算子的谱。
Spectral theory is an important branch of functional analysis in modern times the operator spectra projected from matrix eigenvalue.
通过研究相应算子的谱特征得到该系统解的渐近稳定性。
Asymptotic stability of the solution of this system is obtained by studying spectral properties of the operator corresponding to this system.
通过对积分算子谱的估计，作者给出了一阶线性微分差分方程在边值条件下解的存在唯一性定理。
In this paper, by estimates of spectral of an integral operator, the authors give a theorem on the existence of solutions for first order differential difference equations with boundary condition.
本文引进了有限阶可分介算子的概念，讨论了这类算子的某些性质，特别研究了它的谱性质。
In this paper, we introduce the definition of decomposable operators with finite order. We set down the basic properties of them. Particularly we discuss their spectral properties.
本文研究一类自伴算子的积分形式，利用这种形式证明这类自伴算子的谱集是离散的，然后推出几个性质。
This paper discusses the integral representation of a class of self-adjoint operators. By applying such representation, it is proved that the spectrums of such operators are discrete.
本文利用射影算子、积分算子、乘法算子来证明各种谱的存在性。
In this article, the existence possibility of various spectra is proved with projector operator, integral operator and multiplication operator.
通过对滤子积余弦算子函数及生成元谱性质的讨论，建立了局部等度连续余弦算子函数的谱映象定理。
By discussing the filter product cosine operator function and the spectrum of it 's generator, the spectral mapping theorem for the locally equicontinuous cosine operator function is established.
结论算子范数对于估计有界线性算子乘积与和的谱半径是至关重要的。
Conclusion Norm of operator is very important to estimate the spectral radius of operator.
比较了局部放电的脉冲相位分布谱图和谱图的差异，并计算了各类放电对应的统计算子95％置信区间。
PD pulse phase distribution spectrum was compared with spectrum, and 95% fiducial intervals of statistic operators were also summed up.
运用泛函分析的方法 ，通过分析系统主算子的谱特征 ，给出一类具有备用部件的可修人机系统解的渐近稳定性证明 。
By using functional method, the asymptotic stabitity of a solution of a repairable standby human-machine system is proved, by studing spectral properties of the operator corresponding to this system.
在4.3.4节，我们证明了狄拉克算子在外场中有着对应着无穷远处时零势能极限的自由狄拉克算子的相同的本质谱。
In Sect. 4.3.4 we show that the Dirac operator in an external field has the same essential spectrum as the free Dirac operator provided the potential vanishes at infinity.
线图在图的谱理论研究中起着重要的作用。对一些整谱图，运用一种全新的广义线图算子方法，构造出了一系列无穷多个新的整谱图。
Line graph plays an important role in the study of spectral graph theory. By using the operator generalized line graphs on some integral graphs, a series of infinite integral graphs is constructed.
前者称为微分算子的谱分析，后者称为逆谱问题。
The former is called the spectra analysis of a differential operator and the latter is the inverse spectra problem.
前者称为微分算子的谱分析，后者称为逆谱问题。
The former is called the spectra analysis of a differential operator and the latter is the inverse spectra problem.
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