查询词典 linear operator

Let 〓 be two Hilbert spaces over the same field,and let T:〓a bounded linear operator with closed range.

在1.4中，我们在最一般条件假设下，给出了Hilbert空间上线性有界算子及其最小二乘解的误差分析，从而完整地解决了Hilbert空间算子的扰动理论。

Let A" denote the commutant of a bounded linear operator S on H and R denote the collection of all operators in A" which are compact and upper triangular operators with diagonal sequence being zeros. In this paper, we show that if A"= CI + R, the K_0-group of A" is isomorphic to the integer group.

本文指出若H上的有界线性算子S的换位代数A′=CI+R，其中C是复数域，I是H上的单位算子，R是所有与S可交换的对角线为0的紧上三角有界线性算子的集合，则K_0A′

Let Xand Y be different Banach spaces and 〓Lbe a bounded linear operator,thegeneralized condition number 〓and〓ABA=A,B〓L}are studied.

文章讨论了两类广义条件数的几种表达式，研究了这两类广义条件数之间的关系，并将它们用到算子方程的扰动估计中，推广了Demko[IV.1]中的结果。

In chapter 4, we give the definition of quasi-norm of linear operator with respect to a given bounded set in F* space and study some of its properties.

第四章 在F~*空间上给出线性算子关于一个给定有界集的拟范数的定义，研究它的某些性质。

This method consists of solving a Cauchy problem for a linear operator equation.

3，4」中，提出了解右端数据有扰动的线性算子方程的动态系统方法·实际间题中，算子与右端数据通常是近似已知的。

In Chapter 4, on the basis of introducing the theory of linear operator semigroup and the Cauchy problem in Hilbert space, this dissertation has researched the method on solving solution of distributed parameter system, and the model estimation and optimal control of the nonlinear distributed parameter system.

本文第四章在介绍线性算子半群理论及希尔伯特空间中的柯西问题的基础上，研究了分布参数系统的近似解求解方法，一类非线性分布参数系统的模型辩识和最优控制等问题。

Furthermore, the kernel of a continuous projection ( in fact, a continuous linear operator in general ) is closed.

进一步的，连续投影(事实上，一般的连续线性算子)的核是闭合的。

To sum up, in the paper unified computational methods for solving notwell-posed continuous linear operator equation wore given and there are alsoconvenient for the physical problems.

综上所述，本文中关于不适定连续线性算子方程求解问题的研究，注意到各种物理问题求解的方便性，给出了解决此类问题的统一的计算方法。

In this paper,four aspects of the above problems were studied:Firstly, the problem of solving continuous linear operator equation inseparable Hilbert space is studied .

通过把第一类连续不适定算子方程转换为等价的无穷维方程组，然后利用投影法，给出了解存在唯一的充要条件；给出了连续线性不适定算子方程解析解，解决了不适定情况下解的表示问题，由此给出了算子方程的数值求解公式；进一步证明了，在解不唯一情况下，此表达式给出的解为算子方程的最小范数解，同时表示出了连续线性不适定算子方程的解集。

In this paper, we shall apply this concept to the ring of linear operators on Banach space X and prove that if a linear operator T on a Banach space X is defined in all of X and has finite descent and ascent then there is a Drazin inverse T~D satisfying TT~DT~k=T~k, T~DTT~D= T~D, and T~DT=TT~D for some nonegative integer k.

以后又对方阵的Drazin逆作了深入的研究。它的一些性质可以参阅。同时对它的应用也作了许多研究，例如可以把Drazin逆的概念应用到Markov过程、线性微分方程组、差分方程组和最优控制等方面。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。