5.
WEAK TYPE (H ,L ) ESTIMATE FOR COMM UTATOR OF - W u Huox iong; Zhang Pu
L et L8 , b be the commutato r generalized by the n2dimensionalM arcink iew icz integral
L8 and a funct ion b∈BMO (Rn). It is p roved that L8 , b is bounded from the Hardy space H 1 (Rn)
into the w eak L 1 (Rn) space.
9.
Restricted Edge Connectivity of Regular Graphs - 欧见平
Abstract An edge cut that separates the connected graph into components with order at least two is
restricted edge cut. The cardinality of minimum restricted edge cut is restricted edge connectivity. Denote byλ′
( G) the restricted edge connectivity, then λ′( G) ≤ξ( G) where ξ( G) is the minimum edge degree. G is
called maximal restricted edge connected if the equality in the previous inequality holds. It is proved in this paper
that : every k - regular connected graph G with k ≥2 and | G| ≥4 is maximal restricted edge connected if
k > | G| P2. It is also exemplified that...
10.
整函数及其线性微分多项式的公共函数 - 郑晓刚; 严荣沐
摘要: 设f 是整函数,如果f 与其线性微分多项式L ( f ) 具有两个IM非零公共小函数,那么能得到一个一般关系式.
从而解决了李平与杨重骏的猜测.
Abstract : Let f be an entire function , if f and its linear differetial polynomialin L ( f ) have two IM nonzero
common small functions , then we can get a general relation. This result solves a conjecture of Ping Li and Yang C
C.
11.
有界域上具有离散核的Cauchy 公式和方程 - 黄玉笙; 林良裕
摘要: 设D 是Cn 空间中具有C(1) 边界5D 的有界域,本文利用D 上一个局部有限的可数强拟凸开复盖,定义了D 上
一个新的局部全纯的σ点有限的单位分解,建立了D上一个更一般的具有离散局部全纯核的Cauchy积分公式并获得D
上52 方程的具有离散核的解的积分表示.
Abstract : Let D be a bounded domain with C(1) boundary in Cn . The authors use the locally finite open coverring of
the countable strictly pseudoconvex to define a new partitions of unity of σpoint finite local holomorphic , constructed a
generalized Cauchy integral formula with discrete local holomorphic kernel on the bounded domain D and applied it to
solving the 52equation.
12.
一类周期全纯自同构的线性化 - 严荣沐
摘要: 该文证明了一类周期全纯自同构映射与线性映射同构, 而由这类全纯自同构映射生成的
子群在A u tCn 中是稠密的.
Abstract: The art icle p roves that each m ap in a class of periodic au tomo rph ism s is con ju2
gate to a linear one, w here the subgroup generated by th is class of au tomo rph ism s is den se
in A u t Cn .
13.
完备随机内积模中的Friedrichs 定理 - 郭铁信; 倪丹
摘要: 完备随机内积模是Hilbert 空间的随机推广. 最近,经典的Riesz 表示定理已经被推广到完备随机内积模上,在此
基础上本文将Hilbert 空间上经典的Friedrichs 定理推广到完备随机内积模上. 首先,证明完备随机内积模上任一正Her2
mite 型惟一地对应一个正自共轭算子. 值得指出的是:完备随机内积模上Friedrichs 定理的证明中所涉及的一系列基本概
念与方法都是以随机共轭空间理论为出发点的,与经典情形完全不同.
Abstract : The notion of a complete random inner product module is a random generalization of that of a Hilbert space. Recently ,
the classical Riesz representation theorem on Hilbert spaces has been generalized onto complete random inner product modules ,in this
paper the classical Friedrichs theorem on Hilbert spaces is generalized onto complete random inner product modules. First ,it is proved
that a positive Hermite form corresponds uniquely to a positive self2adjoint operator in a complete random inner product module ,then
this result leads directly to the proof of the main result of...
14.
完备随机内积模上的Hellinger2Toeplistz 定理 - 郭铁信; 李克华
摘要: 在新近发展起来的随机共轭空间理论基础上,利用完备随机内积模上的Riesz 表示定理,证明了如下结论:设( S ,
χ) 是任一完备随机内积模, T : S vS 是S 上任一模同态. 若X Tp , q = Xp , Tq , Pp , q ∈S ,那么T 是几乎处处有界的.
Abstract : The notion of a complete random inner product module is a random generalization of that of a Hilbert space. The Hell2
inger2Toeplistz theorem in Hilbert spaces is a basic and useful tool for linear operators. In this paper ,the basic theorem was general2
ized onto complete random inner product modules ,and the following conclusion was achieved. i. e. ,Let ( S ,χ) be a complete random
inner product module and T : S v S...
15.
完备随机内积模上稠定模同态的共轭算子 - 郭铁信 ; 孟永森
摘 要 对定义在完备随机内积模的稠子模上的模同态引入了共轭算子的概念并讨论其基本
性质, 尤其证明了共轭算子的闭性.
Abstract The notion of the adjoint operator of amodule homomorph ism defined on a densely submodule of
a comp lete random inner p roduct module is introduced and discussed, in particular the closedness of adjoint
operators is p roved.
16.
完备随机赋范空间中几乎处处有界线性算子的几个基本结果 - 郭铁信; 金国华
摘要: 在随机度量理论的新版本下,改进并重新证明了如下结论:设( S1 , X1 ) 和( S2 , X2 ) 均为数域K 上以(Ω, A ,μ) 为基的
随机赋范空间,当S2 是完备时, ( B ( S1 , S2 ) , X) 亦为完备的,其中( B ( S1 , S2 ) , X) 为所有定义在S1 上取值于S2 中的几乎
处处(简写为a. s. ) 有界线性算子所成的随机赋范空间. 并在此基础上证明了当T 为完备随机赋范空间S 上a. s. 有界线
性算子时,如果μ({ω∈Ω: X T (ω) ≥1} ) = 0 ,则算子I - T 有a. s. 有界逆算子. 此外还引入了在完备随机赋范模中几乎处处
有界线性算子的谱的概念,并指出关于这种谱研究中的本质困难.
Abstract : Under the new version of random met ric theory ,this paper improved and proved the conclusion that if ( S1 , X1 ) and
( S2 , X2 ) are two Random Normaled spaces over the scalar field K with...
17.
随机赋范模中的分离定理 - 郭铁信; 肖海霞
摘要: 证明了如下基本的分离定理设( S , X) 为任一随机赋范模, G为S 中的任一模凸闭集, p0 ∈S \ G,那么存
在S 上一个几乎处处有界的随机线性泛函f 使得(Ref ) ( p0) > ∨{ (Ref ) ( g) | g ∈ G}
Abstract : In this paper ,we show the following basic separation theorem: let ( S ,χ) be a random normed module over
the scalar field Kwith base (Ω , A ,μ) ( aσ2finite measure space) , G < S a closed M2convex set and p0 ∈S \ G, then
there exists a nonzero a. s . bounded random linear functional f∶S vL (μ, K) such that (Re f ) ( p0) > ∨g ∈G (Re f...
18.
Survey of Recent Developments of Random Metric Theory and Its Applications in China - 郭铁信
Abstract: The central purpose of this paper is to present a complete account of the principal results and
ideas currently available in the course of the development of random metric theory and its app lications in
China. This paper is divided into ten sections. Section 1 is devoted to a brief introduction of the background
of our work—the theories of probabilistic metric spaces and random metric spaces; Section 2 to some
prelim inaries from random functional analysis and abstract space2valued measurable functions. Section 3 is
devoted to a survey of the global relationsh ip between random functional analysis and original random metric
theory ( called F...
19.
随机度量理论及其应用 - 郭铁信
摘要: 扼要地总结作者近10 多年来在从事随机度量理论及其应用过程中所获得的主要结果与思
想, 包括1) 关于随机度量理论与随机泛函分析的整体关系, 并给出对应于随机度量理论标准定义的
随机共轭空间理论(此部分工作系作者最近的成果) ; 2) 随机度量理论的一个新的版本及对应于这个
版本下随机共轭空间理论的基本结果; 3) 关于随机共轭空间的表示定理; 4) 关于完备随机赋范模为
随机自反空间的特征化定理; 5) 结束语.
Abstract: The cen t ral pu rpo se of th is paper is to give a b rief su rvey of the p rincipal resu lt s
and ideas the au tho r ob tained in the cou rse of undertak ing the study of random m et ric theo ry
and it s app licat ion s. Th is paper is divided in to f ive part s: Part 1 is devo ted to the global
relat ion sh ip betw een random m et ric theo ry...
1.
