反对角算子矩阵及其平方的(ω)性质的摄动

设H为复的无限维可分的Hilbert空间,B(H)为H上的有界线性算子的全体.若σ_a(T)\σ_(ea)(T)=π_(00)(T),则称T∈B(H)满足(ω)性质,其中σ_a(T)和σ_(ea)(T)分别表示算子T的逼近点谱和本质逼近点谱,π_(00)(T)={λ∈isoσ(T):0dimN(T-λI)∞}.T∈B(H)称为满足(ω)性质的摄动,若对任意的紧算子K,T+K满足(ω)性质.本文证明了反对角算子矩阵及其平方具有(ω)性质的摄动的等价性.     

多维非退化扩散过程的象集与图集的一致Hausdorff维数

设X(t)=X(0)+∫^t_0α(X(s))dB(s)+∫^t_0β( X(s))ds为一d(d≥3)维非退化扩散过程。令X(E)={X(t): t∈E}, GRX(E)={(t,X(t)): t∈E}，该文证明了：对几乎所有ω：E B([0,∞)),有dimX(E,ω)=dimGRX(E,ω)=2dimE,这里dimF表示F的Hausdorff维数。     

广义幂等算子差的可逆性

设P, Q为Hilbert空间H上的幂等算子, 关于算子$P$的广义幂等算子类ω(P)定义为ω(P)={A∈B}(H): A²=αA+βP, AP=PA=A,P²=P,∨α, β∈C}. 对任意A ∈ω(P), B∈ω(Q)使得A²=αA +βP, B²=mB+nQ,βn≠ 0, 得到了如下的结论: 值域R(PQ)是闭的充要条件是值域R(AB)是闭的; 如果P-Q是可逆的, 则A-B是可逆的.     

由分数次导数所确定的L2(T)中的一元周期函数类在Lq(T)中的相对宽度

作者研究了相对宽度K_n(W₂^α(T), MW₂^β(T), L₂(T)), T=[0,2π], 确定了使等式K_n(W₂^α(T), MW₂^β(T), L₂(T))=d_n(W₂^α(T), L₂(T))成立的最小M值, 得到了相对宽度K_n(W₂^α(T), W₂^α(T), L_q(T))的渐近阶, 其中α≥β>0, 1≤q≤∞, K_n(., ., L_q(T)) 和 d_n(., L_q(T))分别表示Kolmogorov意义下L_q(T)尺度下的相对宽度和宽度, MW_p^α(T), 1≤ p≤∞, 表示有如下卷积表达式的2π 周期函数类, f(t)=c+(B_α* g)(t),c∈ R, B_α*g 表示 B_α 和g 的卷积, g∈L_p(T) 满足∫₀^2πg(τ)dτ=0 和||g||_p≤M, B_α∈ L₁(T) 有如下Fourier展开: B_α(t)=1/2π∑' _{k∈ Z}(ik)^-αe^ikt,∑^'表示去掉 k=0的项.     

一阶微分方程周期边值问题的解的存在性

该文用拓扑度理论证明了一阶微分方程周期边值问题关于下解与上解之间解的存在性的两个定理，这里下解α(t)与上解β(t)可以不满足关系α(0)≤α(2π)，β(0)≥β(2π)     

Triebel-Lizorkin空间上二阶有限时滞退化微分方程的适定性

本文在周期Triebel-Lizorkin空间F_(p,q)~s(T;X)上研究二阶有限时滞退化微分方程(Mu')'(t)+αu'(t)=Au(t)Gu'_t+Fu_t+f(t)(t∈T:=[0,2π]),u(0)=u(2π),(Mu')(0)=(Mu')(2π)的适定性.利用Triebel-Lizorkin空间上算子值傅里叶乘子定理,给出上述方程是F_(p,q~-)~s适定的充要条件.     

多重C~*-动力系统在Hilbert C~*-模上的膨胀

研究了多重C~*-动力系统在Hilbert C~*-模上表示的膨胀.设(A,α)是一个多重C~*-动力系统,(π,T,E)是(A,α)的行压缩协变表示,证明了存在(π,T,E)的等距膨胀(ρ,V,F).     

Kobayashi’s and Teichmuller’s Metrics and Bers Complex Manifold Structure on Circle Diffeomorphisms

Given a modulus of continuity ω,we consider the Teichmuller space TC1+ω as the space of all orientation-preserving circle diffeomorphisms whose derivatives are ω-continuous functions modulo the space of Mobius transformations preserving the unit disk.We study several distortion properties for diffeomorphisms and quasisymmetric homeomorphisms.Using these distortion properties,we give the Bers complex manifold structure on the Teichm(u| ")ller space TC^1+H as the union of over all0 <α≤1,which turns out to be the largest space in the Teichmuller space of C1 orientation-preserving circle diffeomorphisms on which we can assign such a structure.Furthermore,we prove that with the Bers complex manifold structure on TC^1+H ,Kobayashi’s metric and Teichmuller’s metric coincide.     

非线性四阶周期边值问题的最优正解

该文使用锥不动点定理研究了四阶周期边值问题u⁽⁴)-m⁴u+F(t, u(τ(t)))=0, 0 < t < 2π, u⁽ⁱ⁾(0)=u⁽ⁱ⁾(2π),~ i=0,1, 2, 3, 这里 F: [0,2π ]×R⁺→R⁺ 和τ: [0, 2π]→[0, 2π] 是连续的, 0-7.     

The isometric extension problem in the unit spheres of l<Superscript>p</Superscript>(Г) (<Emphasis Type="Italic">p</Emphasis> >1) type spaces

In this paper, we first derive the representation theorem of onto isometric mappings in the unit spheres of l ^p (Г) (@#@(p >) 1,p ≠ 2 type spaces, and then we conclude that such mappings can be extended to the whole space as real linear isometries by using the previous result of the author.     

On the precise growth, covering, and distortion theorems for normalized biholomorphic mappings

In this paper, we consider a normalized biholomorphic mapping f(x) defined on the unit ball in a complex Banach space, where the origin 0 is a zero of order k+1 of f(x)−x. The precise growth and covering theorem for f(x) is obtained when f(x) is a starlike mapping or a starlike mapping of order α. Especially, the precise growth and covering theorem for f(x) is also established when f(x) is a quasi-convex mapping. Moreover, the precise distortion theorem for f(x) is given when f(x) is a convex mapping. Our result includes many known results.     

广义Bochner-Riesz乘子的等价性及其应用——献给陆善镇教授75华诞

本文研究下面这两个函数,（1-｜x｜^ρ1）＋^α和（1-｜x｜^ρ2）＋^α,其中ρ1,ρ2和α均为正实数,文献上称这类函数为广义Bochner-Riesz乘子.本文将证明,当α给定时,对任意的ρ1〉0和ρ2〉0,这两个函数作为乘子,其乘子算子的L^p有界性和Hp有界性是等价的.     

p -级数域重排特征系统的(C, α)}和

令G_p 为p级数域.在文献[9]中, G.Gát 和 K.Nagy 已经证明p级数域的重排特征系统的(C,1)极大算子是强 (q, q)型(1 α_n f 几乎处处收敛于f.     

B_p上α凸映照

该文对当α≥0时给出Bp上α凸映照与星形映照之间的关系，给出一些Bp上α凸映照的例子.     

Distortion theorem for Bloch mappings on the unit ball <Emphasis Type="Italic">ℬ</Emphasis><Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>

In this paper, we obtain a version of subordination lemma for hyperbolic disk relative to hyperbolic geometry on the unit disk D. This subordination lemma yields the distortion theorem for Bloch mappings f ∈ H（B^n） satisfying ｜｜f｜｜0 = 1 and det f＇（0） = α ∈ （0, 1], where｜｜f｜｜0 = sup{（1 - ｜z｜^2 ）n＋1/2n det（f＇（z））[1/n ： z ∈ B^n}. Here we establish the distortion theorem from a unified perspective and generalize some known results. This distortion theorem enables us to obtain a lower bound for the radius of the largest univalent ball in the image of f centered at f（0）. When a = 1, the lower bound reduces to that of Bloch constant found by Liu. When n = 1, our distortion theorem coincides with that of Bonk, Minda and Yanagihara.     

复平面上解析Banach空间的拟不变子空间

讨论复平面上解析Banach空间具有任意指标的拟不变子空间的存在性问题.首先给出一类复平面上解析Banach空间存在任意指标拟不变子空间的判定定理.作为应用,证明了Fock型空间F~p(C)={f∈Hol(C):1/π∫_C|f(z)|~pe~(-|z|~2)dA(z)+∞,1≤p+∞}与Hilbert空间H={f∈Hol(C):1/π∫_C|f(z)|~2e~(-|z|)dA(z)+∞}具有任意指标的拟不变子空间.     

有一个实现包含Kr +1的可图序列

设K _{r +1}是一个r +1个顶点的完全图. 一个可图序列π =(d₁, d₂,…, d_n)称为是蕴含K _r+1 -可图的, 如果π有一个实现包含 K _{r +1}作为子图. 该文进一步研究了蕴含K _{r+1 -}可图序列的一些新的条件, 证明了这些条件包含文献[14,10,11]中的一些主要结果和当n≥5r/2 +1时,σ(K _r+1, n)之值(此值在文献[2]中被猜测, 在文献[6,7,8,3]中被证实). 此外, 确定了所有满足n≥5, d₅≥4 且不蕴含K₅ -可图序列π=(d₁, d₂,…, d_n)的集合.     

奇异积分算子q-变差的定量最优加权估计

本文将定量最优A_p权理论推广到联系于ω-Calderón-Zygmund算子的q-变差情形.这些结果利用了Lerner最新给出的稀疏控制方法来控制q-变差,和Hyt?nen等关于q-变差的最优加权成果相比,本文涉及的ω仅需满足Dini条件,并且其截断是非光滑的.     

与星象函数有关的拟共形近于凸调和映射

讨论了一类解析部分为星象函数的拟共形近于凸调和映射的基本性质,得到了此类映射的系数不等式、积分表达式、增长定理、面积定理与部分和的近于凸半径.     

Universal C*-algebras defined by completely bounded unital homomorphisms

Suppose A is a unital C*-algebra and r 1.In this paper,we define a unital C*-algebra C_(cb)*(A,r) and a completely bounded unital homomorphism α_r:A → C_(cb)*(A,r)with the property that C_(cb)*(A,r)=C*(α_r(A))and,for every unital C*-algebra B and every unital completely bounded homomorphism φ:A→ B,there is a(unique)unital *-homomorphism π:C_(cb)*(A,r)→B such thatφ=πoα_r.We prove that,if A is generated by a normal set {t_λ:λ∈Λ},then C_(cb)*(A,r)is generated by the set {α_r(t_λ):λ∈Λ}.By proving an equation of the norms of elements in a dense subset of C_(cb)*(A,r)we obtain that,if Β is a unital C*-algebra that can be embedded into A,then C_(cb)*(B,r)can be naturally embedded into C(cb)*(A,r).We give characterizations of C_(cb)*(A,r)for some special situations and we conclude that C_(cb)*(A,r)will be "nice" when dim(A)≤ 2 and "quite complicated" when dim(A)≥ 3.We give a characterization of the relation between K-groups of A and K-groups of C_(cb)*(A,r).We also define and study some analogous of C_(cb)*(A,r).