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数学进展
  1985年, 第14卷, 第2期 刊出日期:1985-04-15 上一期    下一期
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广义Calderón Zygmund算子及其加权模不等式
彭立中
数学进展. 1985, 14 (2): 97-115.  
摘要  
本文推广Coifman和Meyer的Calderon-Zygmund算子概念,定义了M-型和θ-型广义Calderon-Zygmund算子,证明了它们的L~p有界性。然后对θ-型Calde-ron-Zygmund算子证明L~p加权模不等式。由于θ-型Calderon-Zygmund算子的广泛性,这就不但对已有的一些算子的加权模不等式给出了新的证明,同时还得到了一系列新的结果,其中包括各种类型的伪微分算子和交换子的加权模不等式。接着讨论具有较高阶光滑性条件的C~N-型Calderon-Zygmund算子,得到H~p到L~p有界性结果。最后通过把Calderon-Zygmund算子推广到向量值函数,并借助Little-wood-Paley理论,对Caifman和Meyer的一类广义伪微分算子和Meyer的一类广义伪微分算子得到加权模不等式。
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研究论文
积分表示理论
G.Choquet
数学进展. 1985, 14 (2): 116-126.  
摘要  
用较简单的函数来表示非常一般的函数的思想是由来已久的。这种思想曾经出现在Cauchy积分公式和 Poisson积分公式中,以后又出现在绝对单调函数的 Bernstein定理、势论的 Martin定理和群论的 Bochner-Weil定理中。这些公式和定理中的每一个都是由其作者用一种适用于他所研究的理论的特殊方法来得到的。直到 Krein-Milman(1940)定理问世以后,人们才期望有可能在一个极为一般的框架中使它们有统一的陈述。但是,Krein-Mil-
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von Neumann代数的因子分类
李炳仁
数学进展. 1985, 14 (2): 127-139.  
摘要  
1929年,von Neumann引入了算子环的概念.现在,人们把它称为von Neumann代数.由于它的重要性与复杂性,这个数学理论已发展成为近代数学的一个热闹的分支. 三十年代,von Neumann与Murray合作,对于von Neumann代数的研究奠定了基础.他们指出,在von Neumann代数中,关键是因子,即中心是平凡的von Neumann代数.事实上.他们提出的“约化理论”,指出任何的von Neumann代数可以表达为因子的连续直接和(“积分”).
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一类非线性演化方程的Bcklund变换与scale变换的关系
黄迅成
数学进展. 1985, 14 (2): 140-142.  
摘要  
Bcklund变换是孤立子数学理论的重要组成部分。由方程的Backlund变换出发常可引出方程的无穷多个守恒律,解的非线性迭加公式以及孤立子解;然而,在Backlund变换的这些功用中,它所含参数的任意性极为重要,因而探讨不同参数的Backlund变换之间的关系是很重要的。本文就李翊神最近得到的一类演化方程的Backlund交换进行类似的讨论,给出了这类方程的Backlund变换与scale变换的关系。
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流形的去核乘积
古志鸣
数学进展. 1985, 14 (2): 143-146.  
摘要  
一个拓扑空间X的k重去核乘积,指的是把乘积空间X~k中全部形如(x,…,x)的点去掉后所得到的子空间.吴文俊在[1]中提出了有限可剖分空间的一个新拓扑不变量,其中包括该空间的去核乘积的伦型,即有限可剖分空间的k重去核乘积的伦型是原空间的拓扑不变量,而且一般非同伦不变.[1]还提出在流形的范畴中,这个新拓扑不变量是否有新的意义的问题.本文指出,对于某一类流形来说,它的k重去核乘积的上同调群、同调群以及同伦
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关于Bernstein-Kantorovi多项式在L_P[0,1]空间中的逼近阶
周信龙
数学进展. 1985, 14 (2): 147-157.  
摘要  
§1.引 言 对于1≤p<∞,以L_p[a,b]表示适合||f||L_p[a,b]={ |f(x)|~pdx}~(1/p)<∞的f全体。记L_∞[a,b]≡C[a,b],||f||L_∞[a,b]=max|f(x)|. 若a=0.b=1,简记||f||L_p[0,1]=||f||L_p·又设 B_p={g:g(x),g’(x),x(1一x)g’(x)∈L_p[0、1]; x(1-x)g’(x)|x=0,1=0},
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典型群上Fourier级数的球求和以及球平均求和
范大山
数学进展. 1985, 14 (2): 158-167.  
摘要  
典型群 U_n,SO(n)及USP(2n)上的 Fourier分析,已由龚昇在[1—6]以及王世坤、董道珍,陈广晓,贺祖琪在[7,8]中系统地研究过.本文是在他们的基础上,对典型群上 Fourier级数的球求和及球平均求和作了进一步的讨论.文章只叙述n阶酉群 U_n上的结论,因为没有实质困难就能在SO(n)和USP(2n)上得到类似的定理.
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关于亏函数的亏量和F.Nevanlinna猜想
李庆忠,叶亚盛
数学进展. 1985, 14 (2): 168-174.  
摘要  
在亚纯函数值分布论的发展中,有一个有名的 F.Nevanlinna猜想.即:若f(z)是有限级λ的亚纯函数,且∑δ(a,f)=2(a是f的亏值),则 (i)λ是1/2的整数倍; (ii)v(f)≤2λ,其中v(f)是f的亏值个数; (iii)亏量δ(a,f)是1/λ的整数倍.
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关于杨重骏之猜想
宫为国
数学进展. 1985, 14 (2): 175-175.  
摘要  
在文[1]中,杨重骏提出了下述两个猜想 猜想1 设p,q为两个非线性的多项式,若p=O q=0,p(z)=1 q’(z)=1, 则p≡q. 猜想2 设f,g为二超越整函数,且 f=0 g=0与 f=1 g=1.若f g,则必有fg≡1,且f≡e~x(z),共中x(z)为一非常数的整函数. 我们认为,猜想1和猜想2都不成立. 我们先来证明猜想1不成立.
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On the Periodic Solution to the Newtonian Equation of Motion
沈祖和
数学进展. 1985, 14 (2): 176-177.  
摘要  
Consider the system of ordinary differential equation u”(t)+grad G(u(t))=p(t),(1)where p:R→R”is continuous and 2π periodic and G:R~π→R has continuous secondorder partial derivatives.The system can be interpreted physically as the Newto-nian equation of motion of a mechanical system subject to conservative internalforces and the periodic external forces.
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Classification of Cartan Matrices of Hyperbolic Type
李旺来
数学进展. 1985, 14 (2): 177-178.  
摘要  
In the theory of finite dimensional semisimple Lie algebras,it is known thatthe Cartan matrix A=(a_(ij))_i~n, i=1 has the following properties: (1)a_(ii)=2,i=1,…,n; (2)a_(ij)≤0 for i≠j,a_(ij)∈Z; (3)a_(ij)=0 a_(ji)=0. Now if a matrix A=(a_(ij))_i~n,j\j=1 satisfies (1),(2),(3),then A is called
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A Necessary and Sufficient Condition for the Complete Reducibility of a g (A)-module
卢才辉
数学进展. 1985, 14 (2): 178-179.  
摘要  
Suppose that A is an n×n complex matrix.The contragredient Lie algebraassociated to matrix A is denoted by g(A). A g(A)-module V is called h-diagonalizable if it admits a weight space decom-position V= V_λ,and dimV_λ<∞. Let P(V)={λ∈h外\*|V_λ≠0} be the set of weightsof V.For λ∈h*,set D(λ)={μ∈h*|μ≤λ}.
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On the Number of p-blocks with Given Defect Groups and Some Applications of the p-power Homomorphism
石生明
数学进展. 1985, 14 (2): 179-181.  
摘要  
In this paper we establish the p-power homomorhism(Lemma 1).By using itwe can generalize Robinson’s results.([1]. J.Algebra 84(1983),493—502.)In addi-tion,we give some applications.Here we only announce the first three results ofthis paper.
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Degree of Rational Approximation in Digital Filter Realization
沈燮昌
数学进展. 1985, 14 (2): 181-182.  
摘要  
In recursive digital filter design,the amplitude characteristic of an ideal filterhas to be translated into a rational function that is pole-free on the closed unitdisk and preferably has real coefficients.This is possible through a causal trans-formation utilizing the tolerance allowance.In this paper we study the degree ofuniform approximation by rational functions.
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Feynman-Kac Semigroups and Evolution Equations (Ⅰ):On the Density Functions of Feynman-Kac Semigroups
马志明
数学进展. 1985, 14 (2): 182-183.  
摘要  
Let(E,E)be a metric space with its Borel-field.Denote by b(E)the totalityof bounded measurable functions on(E,E).Suppose (X_t)_(t≥0) is a Progressivelymeasurable(w.r.t.its natural filtration)Markov process,conservative or non-
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Feynman-Kac Semigroups and Evolution Equations (Ⅱ):Evolution Equations with Discontinuous Potential Terms
马志明
数学进展. 1985, 14 (2): 184-185.  
摘要  
Consider the following Cauchy problem: u/t=Lu+Vu+§ (1) u(0,·)=f (2)where L is the elliptic differential operator we have described in [1].V、§ andf are measurable functions on R~d satisfying the following conditions: (i)V=(sum from k=1 to ~nv)V_k,where V_k∈L_P_K(R~d),1 Related Articles
On the Selection of Subset AR Models
安鸿志
数学进展. 1985, 14 (2): 185-187.  
摘要  
Consider a stationary AR model(see[l]or[2]) y(t)=a_1y(t-1)+a_2y(t-2)+…+a_py(t-p)+e(t) (1)where e(t)is a martingal difference series which is stationary and has finite fourthmoment. If the true values of the parameters a_i,i=i_I,I_2…,i_p,are non-zero,but zero
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An Abstract Critical Point Theorem and Applications
李树杰,王志强
数学进展. 1985, 14 (2): 187-189.  
摘要  
In this paper,we prove a following critical point theorem by using linkmethod in [1]. Theorem 1.1. Let X be a real Banach space,X_1,X_2 be subspaces of X.X=X_1+X_2 and dim X_2=m<+∞,f(x)∈ C~1(X,R)satisfies Palais-Smale conditionand following three conditions: i)There exist ρ>0,β>a such that f|βρηx_1≥β, ii)There exist e∈β_R∩X_1,R>ρ such that
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r-Quantifier Elimination and r-Homogeneous Models
饶炬
数学进展. 1985, 14 (2): 189-190.  
摘要  
The purposes of this paper are: (1)Give a model theoretic condition forthe theory T admitting γ-quantifier elimination.(2)Give a class of models whichcan describe the theory admitting γ-quantifier elimination. Definition. Two models and are γ-equivalent(in notation ≡r )if and satisfy the same sentences of quantifier deepth(quantifier rank) γ. is γ-homogeneous of for any a_1, …,a_n,a_(n+1), b_1,…,b_n A suchthat
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The Degree of Unsolvability of Models
岳其静
数学进展. 1985, 14 (2): 190-191.  
摘要  
The purpose of this paper is to describe the complexity of models by theirdegrees of unsolvability,J.Richter defined the degree of a structure to be deg ()=sup{deg(),deg(R_i),i=1,…,n},Where is a model for afinite language L={R_i,i=1,…,n}and the universe of is a subset of ω. Shepointed out that, according to her definition, there can be models which areisomorphic but their degrees are different.Also,her discussions are restricted tofinite languages and models whose universes are subsets of ω.
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