1) dual operator
对偶算子
1.
A to be determined coefficient method for finding dual operators of hierarchiesof non-linear evolution equations is proposed.
本文提出了寻求非线性演化方程的对偶算子的待定系数法。
2.
The paper has studied the structure of spectrum for dual operators and partial differen- tial operators on locally convex spaces,The main results are as follows: Theorem 1 Let X be a complete barrelled space.
研究了局部凸空间上对偶算子和偏微分算子的谱结构。
3.
Inverse and dual combination operator is defined as a new genetic operator based on respective application study of inverse operator and dual operator,which can improve local searching.
在逆序算子和对偶算子的性能研究基础之上,设计了逆序与对偶组合遗传算子,增强了局部搜索性能。
2) Lipschitz quasi-dual operator
拟对偶算子
1.
The concept of Lipschitz quasi-dual operator of nonlinear Lipschitz operator is introduced;and some results of nonlinear Lipschitz operators are given;that is,the "*"operation depended on nonlinear Lipschitz operators is linear;and the resonance theorem for nonlinear Lipschitz operators still hold.
引入非线性Lipschitz算子的Lipschitz拟对偶算子的概念,从而证明了非线性Lipschitz算子的“*”运算的线性性,作为应用,最后证明了非线性Lipschitz算子的共呜定理。
3) Dual Toeplitz operator
对偶Toeplitz算子
1.
We characterize essentially commuting dual Toeplitz operators with bounded measurable symbols and bounded pluriharmonic symbols on the Bergman space of the polydisk respectively.
在单位多圆盘的Bergman空间上,本文分别刻画了以有界可测函数和有界多重调和函数为符号的本质交换对偶Toeplitz算子。
2.
This paper deals with the dual Toeplitz operators on the orthogonal complement of the Fock space.
本篇硕士论文主要研究Fock空间之正交补空间上以平方可积函数为符号的对偶Toeplitz算子。
3.
We deal with commutativity of dual Toeplitz operators of the unit ball, such as the characterizations of commuting dual Toeplitz operators, essentially commuting dual Toeplitz operators and essentially semi-commuting dual Toeplitz operators.
本文主要研究单位球的Bergman空间上的紧算子,对偶Toeplitz算子的交换性和Nehari型定理以及Hankel算子乘积的有界性和紧性。
4) W~#-dual operator
W#-对偶算子
5) W~×-dual operator
W×-对偶算子
1.
The W~# -dual operator:T~#:Y~#→X~# and W~×-dual operator:T~×:T~#→X~ˇ of a continuous conjugate linear operator:T:X→Y are defined.
讨论了复赋范线性空间上的共轭线性算子,以及这类算子的连续性、有界性与范数,得到了连续共轭线性算子空间CCL(X,Y)与连续线性算子空间B(X,Y)之间的关系;引入并研究了复赋范线性空间X的Wˉ对偶空间X#(=CCL(X,C)),定义了共轭线性算子T:X→Y的W#-对偶算子T#:Y*→X#与W×-对偶算子T×:T#→X*,并讨论了它们的一系列重要性质。
6) Lipschitz dual operator
Lipschitz对偶算子
1.
A new dual space notion of a Banach space, named Lipschitz dual space,is introduced, and within the new introduced space framework, the concept of the Lipschitz dual operator of a nonlinear Lipschitz operator is further defined.
本文引进Banach空间E的一个全新对偶空间概念—Lipschitz对偶空间，并证明：任何Banach空间的Lipschitz对偶空间是某个包含E的Banach空间的线性对偶空间,以所引进的新对偶空间为框架，本文定义了非线性Lipschitz算子的Lipshitz对偶算子，证明：任何非线性Lipschitz算子的Lipschitz对偶算子是有界线性算子。
补充资料：凹算子与凸算子
凹算子与凸算子
concave and convex operators
凹算子与凸算子「阴~皿d阴vex.耳阳.勿韶;.留叮.肠疽“‘.小啊j阅雌口叹甲司 半序空间中的非线性算子，类似于一个实变量的凹函数与凸函数. 一个Banach空间中的在某个锥K上是正的非线性算子A，称为凹的(concave)(更确切地，在K上u。凹的)，如果 l)对任何的非零元x任K，下面的不等式成立: a(x)u。(Ax续斑x)u。，这里u。是K的某个固定的非零元，以x)与口(x)是正的纯量函数; 2)对每个使得 at(x)u。续x《月1(x)u。，al，月l>0，成立的x‘K，下面的关系成立二 A(tx))(l+，(x，t))tA(x)，0
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条