1) norm convergence
范数收敛性
1.
The relationships between the strict convergence and norm convergence,strong convergence as well as weak convergence of a net of bounded linear operators on a Hilbert C*-module are discussed.
讨论了Hilbert C*-模上的有界线性算子网的严格收敛性与范数收敛性、强收敛性、弱收敛性之间的关系,证明了:严格收敛的算子网{Tλ}λ∈Λ的伴随算子网{Tλ*}λ∈Λ也是严格收敛的;严格收敛性是保持加法和数乘运算的;两个严格收敛算子网之积仍是严格收敛的;严格收敛的算子网一定是强收敛的。
2) Lp-norm convergence
Lp范数收敛性
1.
Let(Tk,k∈P)be a series of operators with property Δ,the methods of martingale are applied to consider Lp-norm convergence of a kind of partial sum sequences｛nk=1Tk,f｝.
设(Tk,k∈P)为一列具有Δ性质的算子,本文运用鞅方法考虑了部分和序列{∑nk=1Tkf}的Lp范数收敛性,得到了一些充分条件,所得结果对于研究鞅变换的收敛性问题是很有用的。
3) convergence in norm
依范数收敛
1.
The fundamental relationship between convergence in measure and convergence in norm of sequence of functions {f_n(x)} in L~p is that convergence in norm is able to deduce convergence in measure,however,the inverse proposition is false.
Lp空间中的函数列{nf(x)}依测度收敛与依范数收敛的基本关系是:依范数收敛可推出依测度收敛,但逆命题不成立。
2.
The fundamental relationship between convergence in measure and convergence in norm of sequence of functions {f_n(x)} in integrable function space L~p is that convergence in norm is able to deduce convergence in measure while the inverse proposition is false.
可积函数空间Lp空间中的函数列{fn(x)}依测度收敛与依范数收敛的基本关系:依范数收敛可推出依测度收敛,但逆命题不成立。
4) uniformed convergence of norm
范数一致收敛
1.
The problem of uniformed convergence of norm was discussed with the application of the conclusion.
观察Lipschitz条件与范数等价的命题在形式上的一致性,证明推导了结论:范数可以成为一个压缩映像,并利用这一思想来讨论范数一致收敛的问题。
5) global convergence
大范围收敛性
6) exponential convergence
指数收敛性
1.
The Exponential Convergence and Boundedness of the Solutions for Functional Differential Equations;
泛函微分方程解的指数收敛性及其有界性
2.
A new design method of nonlinear reduced order state observer is proposed,and the exponential convergence is proved for the proposed state observer.
提出一种非线性降维状态观测器设计方案 ,并从理论上证明了状态观测误差的指数收敛性 。
3.
The paper studies the existence and global exponential convergence of alomost periodic solutions for high-order neural networks involving variable delay by applying the theory of fixed point and differential inequality technique,some new criteria on the existence and global exponential convergence of almost periodic solutions are obtained.
利用不动点理论和微分不等式分析等技巧,研究了变时滞高阶神经网络概周期解存在性与全局指数收敛性,并且给出了一些新的判别准则。
补充资料：范数收敛
范数收敛
normal convergence
范数收敛【。口，‘c.洲明笋以;HOpM~朋cxo脚。-c，] 由集合X到赋范空间Y中的有界映射u*:X~Y构成的级数 f=艺。*(l) k，l的如下的收敛性:由这些映射的范数 !{u*l卜s叩{!}u*(x)]1:x“X}构成的正项级数艺二111:*”收敛. 级数(l)范数收敛蕴涵由Y的元素构成的级数艺孔，。*(:)绝对并一致收敛，但反之不然.例如，如果。*:R~R是由。*(x)=sin(二x)/k(对于k(x蕊k+l)和u*(x)=0(对于xeR\[k，k十lJ)定义的实值函数，则级数艺二.。*(x)绝对收敛，然而艺二，}}。*”=工二，l/k发散. 特别地，假定每个“*:R~Y是非紧区间ICR中的分段连续函数且(1)范数收敛，则在I上可以逐项积分: 丁f(。)“:一*暑:丁·*(。)d 0. 尹1设f: 1 xA~Y(这里ICR是一个区间)在I的每个点处具有左、右极限，则反常积分 了，(，;*)‘:，*。， I称为在集合A上是范数收敛的(加订压山yc。训。瞥mt)，如果存在分段连续正函数g:R~R，使得:l)对任一x任I和任一又〔A，有}}f(x;又)”簇g(x);2)积分J，g(:)dt收敛.(2)范数收敛组涵它绝对并一致收敛，但反之不然.
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