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1.
本文用到的基本概念和记号有:(Ω,(?),μ)为任一有限测度空间,其中μ是σ-代数(?)上的非负可数可加标量测度。T 是定向集。(B_τ,τ∈T)是(?)的子σ-代数的单调增加网,τ_1,τ_2∈T,τ_1≤τ_2,则B_(τ_1)(?)B_(τ_2).X 是 Banach 空间,其范数是‖·‖,X~*是 X 的共轭空间。  相似文献   

2.
设X为实Banach空间, T:D(T)(?)X→2X*为极大单调算子, C: D(T)(?)X→X*为有界算子(未必连续),而C(T+J)-1为紧算子.本文在上述假设条件下,通过附加一定的边界条件应用Leray-Schauder度理论研究了下述包含关系:0∈(T+C)(D(T)∩ BQ(0)),0∈(T+C)(D(T)∩ BQ(0));以及S(?)R(T+C), intS(?)intR(T+C)(其中S(?) X*);B+D(?)R(T+C),int(B+D)(?)intR(T+C)(其中 B(?)X*,D(?)X*)的可解性,得出了一些新的结论.  相似文献   

3.
设(M,τ)是非交换的概率空间,(xk)nk=1是L0(M)中的一个自由的随机变量序列.设Φ是[0,∞)上递增的凹函数,满足Φ(0)=0.本文主要研究当xk,1 k n是正随机变量时,τΦ(∑nk=1xk)与这个随机变量序列不交和的Φ-距(τ⊕tr)Φ(∑nk=1xk⊕ek)之间的关系.  相似文献   

4.
假设X={Xt, Xτ, Pμ}是Rd中具有一般分支机制ψ与一般分支率函数A的超扩散.讨论当A满足什么条件时,Rd中有界光滑区域D的首出测度XτD具有绝对连续性.  相似文献   

5.
危纯  娄曼丽 《数学学报》2022,(2):235-242
设M=(m_(ij))是一个b×b阶矩阵且m_(ij)∈{0,1},∑_(M)是矩阵M=(m_(ij))诱导产生的有限型,σ是其上左推移算子.本文主要研究的是有限型动力系统(∑_(M),σ)上的首次返回速度问题.令τ_(k)(x)是点x∈∑_(M)首次返回到包含x的k阶柱集时间,且E_(α,β)={x∈∑_(M):lim inf_(k→∞)(logτ_(k)(x))/k=α,lim sup_(k→∞)(logτ_(k)(x))/k=β}.我们证明了:当M是不可约矩阵时,对任意0≤α≤β≤+∞,集合E_(α,β)的Markov测度要么等于0要么等于1并且具有满的Hausdorff维数.  相似文献   

6.
张佳妮  李建林  王琦 《数学学报》2018,61(4):625-630
设p_1,p_2,p_3∈Z\{0,±1},e_1,e_2,e_3是R~3上标准的单位正交基,由扩张矩阵M=diag[p_1,p_2,p_3]和数字集D={0,e_1,e_2,e_3}确定的自仿测度μM,D是支撑在空间Sierpinski垫T(M,D)上,其对应的Hilbert空间L~2(μM,D)上正交指数系的有限性与无限性问题已经解决.在有限的情形下,空间L~2(μM,D)上正交指数系基数的最佳上界为"4"的猜测还未完全解决.本文构造出了此空间上一列五元素正交指数函数系,说明上述最佳上界为"4"的猜测是错误的.  相似文献   

7.
设μ_(M,D)是由仿射迭代函数系{φ_d(x)=M~(-1)-(x+d)}_(d∈D)唯一确定的自仿测度,它的谱与非谱性质与Hilbert空间L~2(μ_(M,D))中正交指数函数系的有限性和无限性有着直接的关系.本文将利用矩阵的初等变换给出μ_(M,D)正交指数函数系有限性的一个充分条件.由于这个条件只与矩阵M的行列式有关,因此,它在μ_(M,D)的非谱性的判断方面便于直接验证.  相似文献   

8.
Cn中多圆柱上广义Bloch空间的点乘子   总被引:1,自引:1,他引:0  
讨论了Cn(n>1)中多圆柱上广义Bloch空间βp上的点乘子,根据p、q的不同情况得到βp空间到βq空间所有的点乘子,得到(1)当p<1时M(βp)=βp;(2)当p≥1时M(βp)=c;(3)当p>q时M(βp,βq)={0};(4)当p<q<1时M(βp,βq)=βq;(5)当p<1≤q时M(βp,βq)=Jp,q∩βq;(6)当1≤p<q时M(βp,βq)=c.  相似文献   

9.
自仿测度的非谱准则   总被引:1,自引:1,他引:0  
李建林 《数学学报》2017,60(3):361-368
设μ_(M,D)是由仿射迭代函数系{φ_d(x)=M~(-1)(x+d)}_(d∈D)唯一确定的自仿测度,它的谱性或非谱性与Hilbert空间L~2(μ_(M,D))中正交指数基(也称为Fourier基)的存在性有着直接的关系.近年来自仿测度μ_(M,D)的谱性或非谱性问题的研究受到人们普遍的关注.本文给出了判定自仿测度μ_(M,D)非谱性的几个充分条件,所得结果改进推广Dutkay,Jorgensen等人的非谱准则.  相似文献   

10.
C^n单位球上Q_p空间的点态乘子   总被引:1,自引:0,他引:1       下载免费PDF全文
该文研究了C^n单位球上Q_p空间的点态乘子空间M(Q_p),分别给出了M(Q_p)与α Bloch 空间及Dirichlet型空间之间严格精确的包含关系.并相应地讨论了单位球上Q_{p,0}空间的点态乘子.  相似文献   

11.
设R是含有恒等元1的半环,C是R上的中心子半环.Tn(R)是R上的n阶上三角矩阵C-代数.证明了当R是一个幂等元都是中心元的半环时,映射Φ:Tn(R)→Tn(R)是乘法半群自同构当且仅当存在Tn(R)中的可逆矩阵G和R中的半环自同构τ使得A=(aij)n×n∈Tn(R),均有Φ(A)=G-1τ(A)G.这里τ(A)=(τ(aij))n×n,n2.  相似文献   

12.
关于域上矩阵广义逆的加法映射   总被引:3,自引:0,他引:3  
张显  曹重光 《数学学报》2004,47(5):1013-101
假设F是特征不为2的域,令Mn(F)是F上n×n矩阵的集合.本文证明了f是Mn(F)到自身的矩阵{1}-逆或{1,2}-逆的加法保持算子当且仅当f有:(a)f=0;(b)f(A)=εPAτP-1对任意A∈Mn(F),其中P∈GLn(F),τ-为域F的某个单自同态且x(1)=1,ε=±1;(c)f(A)=εP(Aτ)TP-1对于任意A∈Mn(F),其中τ,ε,P如(b)中一样意义.  相似文献   

13.
林振声 《数学学报》1979,22(5):515-529
<正> 考虑拟线性微分方程系 dX/dt=A(t)X十f(t)十μF(X,t,μ),(1)其中A(t)是t的n阶连续方阵,x是n向量,f(t),F(X,t,μ)是各变量的n连续向量,μ真是小参数. 当A(t)是常数方阵,f(t),F(X,t,μ)是t的一致概周期向量函数,Coddington,Levinson,等人建立了(1)的周期解的存在定理.此可参考[1]和[2].对A(t)为常数方阵,f(t),F(X,t,μ)是t的一致概周期向量函数,更进一步建立了(1)的概周期解的存在定理.  相似文献   

14.
A functional system P is considered, whose elements are functions realized by the so-called finite automata and known as the boundedly determinate functions (B. D. functions) and whose operations are known as the operations of superposition. The system \(\mathfrak{M}\) of B.D. functions is called A-complete if, for an arbitrary B. D. function and for every natural number τ>0, we can obtain (with the help of the operations of superposition) a B. D. function coinciding with the given one of all the words of length τ from the B. D. Functions of the system \(\mathfrak{M}\) . The question is: does there exist an algorithm for deciding the A-completeness of an arbitrary finite system of B. D. functions ? It is shown that such an algorithm does not exist (see [4]).  相似文献   

15.
张素诚 《数学学报》1958,8(1):102-131
<正> 多面体的伦型鉴定问题,已经有过许多拓扑工作者的研究.J.H.C.Whitehead找到 A_n~2多面体的伦型和正则上同调环头(n=2)或正则上同调系统类(n>2)间的一一对应.他和 S.Machane 发见“三型”所对应的代数构造,于是引起(?)  相似文献   

16.
We give a simple proof of a mean value theorem of I. M. Vinogradov in the following form. Suppose P, n, k, τ are integers, P≥1, n≥2, k≥n (τ+1), τ≥0. Put $$J_{k,n} (P) = \int_0^1 \cdots \int_0^1 {\left| {\sum\nolimits_{x = 1}^P {e^{2\pi i(a_1 x + \cdots + a_n x^n )} } } \right|^{2k} da_1 \ldots da_n .} $$ Then $$J_{k,n} \leqslant n!k^{2n\tau } n^{\sigma n^2 u} \cdot 2^{2n^2 \tau } P^{2k - \Delta } ,$$ where $$\begin{gathered} u = u_\tau = min(n + 1,\tau ), \hfill \\ \Delta = \Delta _\tau = n(n + 1)/2 - (1 - 1/n)^{\tau + 1} n^2 /2. \hfill \\ \end{gathered} $$   相似文献   

17.
Letμ n, n = 0, 1, ..., be a Galton-Watson process, and τx + 1 the instant of first crossing of the level x by the process. A limit theorem is proved for the joint distribution of the random variables $$\tau _x ,x - \mu _{\tau _x } ,\mu _{\tau _x + 1} - x(x \to \infty )$$ on the assumption that Mμ1 In (1 + μ1) < ∞.  相似文献   

18.
On a manifold of dimension at least six, let (g, τ) be a pair consisting of a Kähler metric g which is locally Kähler irreducible, and a nonconstant smooth function τ. Off the zero set of τ, if the metric \({\widehat{g}=g/\tau^{2}}\) is a gradient Ricci soliton which has soliton function 1/τ, we show that \({\widehat{g}}\) is Kähler with respect to another complex structure, and locally of a type first described by Koiso, and also Cao. Moreover, τ is a special Kähler–Ricci potential, a notion defined in earlier works of Derdzinski and Maschler. The result extends to dimension four with additional assumptions. We also discuss a Ricci–Hessian equation, which is a generalization of the soliton equation, and observe that the set of pairs (g, τ) satisfying a Ricci–Hessian equation is invariant, in a suitable sense, under the map \({(g,\tau) \rightarrow (\widehat{g},1/\tau)}\) .  相似文献   

19.
Let C be a category with inverse limits. A category xis called an A-topos if there is a site (?, τ), i.e. a small category ? together with a Grothendieck topology τ such that xis equivalent to the category Shτ[C0. A] of τ-sheaves on C with values in C. If xis an C-topos, then so is Shτ'[?0, x] for any site (?', τ'). It is shown that if for every site (?,τ) the associated sheaf functor from presheaves to τ-sheaves with values in A exists (and preserves finite inverse limits), then the same holds if Ais replaced by any A-topos x. Roughly speaking, the main result is that for a site (?,τ) the associated sheaf functor [?0, A] → Shτ [?0, A] exists and preserves finite inverse limits, provided A has filtered direct limits which commute with finite inverse limits, e.g. if A is a Grothendieck category or a category of sheaves with values in a locally finitely presentable category [8. 7.1]. Analogous results hold in the additive case.  相似文献   

20.
Let z=∞ be the only irregular singular point of the linear differential equation $$(D)w^{(n)} + P_{n - 1} (z)w^{(n - 1)} + \cdots + P_o (z)w = 0$$ with rational coefficients pj(z). If w is a multivalent and irregular solution of (D), we define the index I(τr,W), τ ∈ (0,1), of a branch W of w in the plane cut along a half ray. If r→∞, I(τr,W) possesses a finite number of aymptotic directions being exactly the asymptotic directions of the points z with maximal possible modulus of W(z). It follows that each branch W is of mean type σ(W)=|d|/λ in each sector containing an asymptotic direction of I. The possible values of the order of growth λ=λ(W)<∞ and the constant d are given by the PUISEUX-diagram of (D).  相似文献   

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