线性算子

This dissertation first presents a simple introduction of some important basic problems ofoperator approximation theory,and history and research status of wavelet theory.

全文首先介绍了算子逼近理论的一些重要基本问题以及小波理论发展的历史和现状，指明了线性正多项式算子逼近收敛阶的受限性。

In this paper,we study the boundedness of multilinear commutators of singular integral operators and fractional integral operators with smooth functions.

本文主要研究奇异积分算子和分数次积分算子与光滑函数生成的多线性交换子的有界性问题。

The author investigates simultaneous approximation by Gama operators and the rate of pointwise convergence by new Gamma type operators.

本论文讨论了Gamma算子的同时逼近，Gamma算子线性组合同时逼近的等价定理以及新的Gamma型算子的逼近速度。

In this paper,we build symplectic structure of 2-nd order and high order singular differential operators on infinite interval, we construct a symplectic space by the maximal and minimal operator domain .

本文研究了无穷区间上二阶、高阶奇型微分算子的辛结构，利用最大与最小算子域构造了一个辛空间，用辛空间中的线性流形来刻画定义在无穷区间上二阶、高阶奇型对称微分算子的自共轭扩张问题。

In this paper, we will introduce the weighted modulus of smoothness and the weighted K-functional to discuss the direct and the converse theorems, the local saturation results on the simultaneous approximation on an infinite interval with Jacobi-weight by the integral operator, the lin...

本文利用带权光滑模与带权K--泛函讨论定义在无穷区间上的积分型算子Gamma算子线性组合对空间L_∞(0，∞)中函数的带Jacobi权同时逼近的正逆定理以及局部饱和结果，还讨论了Gamma算子的强逆不等式。

In chapter 3, the problems of constructing finite-dimensional functional linear invari-ant spaces under a given differential operator as well as an inverse problem concerning thedescription of all operators possessing a given invariant space are investigated.

第三章中讨论了基于算法产生的两个互逆问题，即(1)构造在已知的微分算子下不变的有限维线性函数空间；(2)讨论拥有相同线性不变空间的微分算子的一般表达式。

By introducing the general notion of nonwandering operator semigroup T and utilizing a basic result in normed linear space,the nonwandering property of T=e~ is investigated with the constructive method.

通过给出一般算子半群T的非游荡性概念，利用赋范空间的一个基本结果和直接的构造法证明了具有变系数的线性发展方程的强连续解半群T=etA在适当的条件下是非游荡的；另外，通过对C-半群T概念的引进，定义了一个无界算子半群etA，进一步证明了这二者关于非游荡性的联系；最后给出了一个无界算子半群etP关于非游荡性理论的刻画，其中P是微分多项式。

In chapter5, the serial properties of numerical range of operator polynomial are put firstly. Secondly, the relation between numerical range of operator polynomial and n-numerical range are considered. Thirdly, in the light of matrix norm, matrix singular value, the regions and bounds of numerical range and spectrum of operator polynomial are dicussed carefully.

第五章研究了算子多项式数值域的性质、算子多项式数值域与n-次数值域的关系，特别地利用矩阵范数、矩阵的奇异值、非负矩阵的理论、友矩阵为工具，给出了算子多项式数值域及谱的范围全面刻画，并深刻地研究了算子线性束的正则性的等价条件及谱分布。

Linear edge detection operator can implement the one to one mapping of edge detection operator to edge type, that is, one kind of edge detector can only detect one kind of edge.

线性边缘检测算子，只能实现边缘检测算子到边缘类型的一一映射，即一种边缘检测算子只能检测一种边缘类型。

In which the second order degenerate equations associated with square sum operators of Hormander vector fields are the most important classes. People are used to calling them subelliptic operators because they have properties similar to that of classical Laplacian.

由于该算子具有与经典Laplace算子类似的次椭圆性质，人们习惯上把由向量场构成的二阶线性及非线性算子通称为次椭圆算子，相应的方程称为次椭圆方程。

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。