非齐次对称特征值问题

引言 用SR~(n×n)表示所有。n×n实对称矩阵的集合。R~n表示n维线性空间。||·||_2表示向量的Euclid范数或矩阵的谱范数。 本文研究如下问题: 问题ISEP 给定矩阵A∈SR~n×n和向量b∈R~n,求实数λ和向量X∈R~n使得 AX=λX+b, (1) ||X||_2=1. (2) 若b=0,则问题ISEP就是通常的实对称矩阵特征值问题,若b≠0,则问题ISEP称为非齐次对称特征值问题,使(1)和(2)式成立的数λ和向量X分别称为非齐次特征值和相应的非齐     

Riemann-Stieltjes算子的本性范数

本文建立在从Hardy空间H~p到Zygmund型空间Z_μ的Riemann-Stieltjes算子I_(g,φ)和J_(g,φ)的有界性和紧性的特征的基础上,构造了H~p中一些检验函数,运用本性范数的定义与解析函数的性质,给出了算子I_(g,φ)和J_(g,φ)本性范数的估计.     

泛函微分方程中的广义拉什密辛型定理

设R~n为实的n维线性向量空间,C=C([-r,0),R~n)表示映照区间[-r,0)到R~n的连续函数所成的巴拿哈空间,其中r≥0。对φ∈C,取范数|φ|=sup |φ(θ)|(-r≤θ≤0)。记C_H={φ:φ∈C,|φ|≤H}。若σ∈R,A>0,x∈C([σ-r,σ A,R~n),则当t∈[σ,σ A]时。x_t是由x_t(θ)=x(t θ),-r≤θ≤0所定义,故x_t∈C。 现考虑滞后型的泛函微分方程     

关于corona(日冕)问题

设Δ={|z|<1},H~∞(Δ)表示Δ上一切有界解析函数全体所组成的函数族.它是一个Banach代数,因若f和g∈H~∞ (Δ),则fg∈H~∞(Δ),且||fg||_∞≤||f||_∞·||g||_∞.设对单位圆内任何一点z,令M_z={f∈H~∞(Δ):f(z)=0},则M_z是H~∞ (Δ)的一个极大理想.设 表示 H~∞(Δ)的极大理想空间,则它在弱拓扑下成为一个紧致的Hausdorff空间.若对z,|z|<1,则点赋值     

Marcinkiewicz积分交换子的加权有界性(英文)

本文应用加权Hardy空间H_ω~p(R~n)上的原子分解理论,研究了由函数b∈Λβ(R~n)(0<β≤1)与Marcinkiewicz积分μ_Ω生成的交换子μ_Ω~b的有界性;证明了μ_Ω~b是从L~q(ω~q)到L~q(ω~q)有界的,从L~1(|x|γ(n-β)/n)到弱L(n/n-β)(|x|~γ)有界的,且从H~p(ω~p)到L~q(ω~q)有界的,这里1/p-1/q=β/n.     

由生成函数构成的梯度投影法

本文利用生成函数给出一个梯度投影算法模型,统一处理了一类梯度投影算法的收敛性问题.考虑非线性规划问题(P),其中M={x∈R~n|a_j~Tx=b_j,j∈L_1;a_j~Tx≤b_j,j∈L_2},a_j∈R~n,b_j∈R,j∈L=L_1∪L_2.f:R~n→R,f∈C~1.对于     

定向集指标非交换鞅的几种收敛性

本文研究了定向集指标非交换鞅的几种收敛性.利用非交换鞅的理论,得到了如下结果:设{xα,Mα}α∈I是一个定向集指标的非交换鞅.则{xα}依L1范数收敛(或弱收敛)的充要条件是{xα}一致可积且满足条件(B):对任意的ε0,存在投影e∈M,使得对任意的y∈M,y≤1及任意的α∈I,有|τ(exαey)|ε.当1p∞时,{xα}依Lp范数收敛(或弱收敛)的充要条件是{xα}在Lp(M)中依Lp范数有界.这也等价于存在一个x∞∈Lp(M),使得xα=Eα(x∞)(α∈I).推广了交换情形中的相应结果.     

求地震反演的I_1模极小化模型的解

1 引 言 在文[1]中提出了地震反演的l_1模极小化模型是: min ψ(x)=||x||1, (1.1) s.t. Ax=b,其中A∈R~(m×n),m相似文献   

求解广义混合单调变分不等式的预解算子方法

1引言设R~n表示n维欧式空间,‖·‖和＜,＞分别表示R~n中的范数和内积,K为R~n中的非空闭凸集,(?)是R~n到R∪{ ∞)的算子．对于给定的非线性算子T,g：R~n→R~n,考虑下面的广义混合变分不等式,记为GMVI：求u∈R~n满足(Tu)~T(g(v)-g(tu)) (?)(g(v))-(?)(g(u))(?)0,(?)g(v)∈R~n．(1)假如(?)是R~n中非空闭凸集K的指标集,即,(?)(u)≡I_k(u)=(?)．此时GMVI等价于下面的广义变分不等式：求u∈R~n,g(u)∈K满足     

奇异积分交换子的加权Hardy型估计

T_b表示由加权Lipschitz函数b∈Lip_β(μ)(0β1)与Calderon-Zygmund奇异积分算子T生成的交换子.当μ∈A_1,n/(n+β)p≤1时研究了T_b在经典加权Hardy空间H~p(μ))上的有界性质,在端点p=n/(n+β)处研究了T_b在加权Hardy空间上的弱型估计.     

Littlewood-Paley算子的交换子的有界性

设n/(n+ε) 相似文献   

振荡奇异积分的L~p有界性

文中讨论了振荡奇异积分:其中对满足一定凸性条件的P以及Ω∈L~q(S~(n-1))(q>1),证明了T在L~P(R~n)上有界,p>1.     

Hardy spaces H_L~p(R~n) associated with operators satisfying k-Davies-Gaffney estimates

Let L be a one-to-one operator of type ω having a bounded H∞ functional calculus and satisfying the k-Davies-Gaffney estimates with k ∈ N. In this paper, the authors introduce the Hardy space HLp(Rn) with p ∈ (0, 1] associated with L in terms of square functions defined via {e-t2kL}t>0 and establish their molecular and generalized square function characterizations. Typical examples of such operators include the 2k-order divergence form homogeneous elliptic operator L1 with complex bounded measurable coefficients and the 2k-order Schrdinger type operator L2 := (-Δ)k + Vk, where Δ is the Laplacian and 0≤V∈Llock(Rn). Moreover, as an application, for i ∈ {1, 2}, the authors prove that the associated Riesz transform ▽k(Li-1/2) is bounded from HLip (Rn) to Hp(Rn) for p ∈ (n/(n + k), 1] and establish the Riesz transform characterizations of HL1p (Rn) for p ∈ (rn/(n + kr), 1] if {e-tL1 }t>0 satisfies the Lr-L2 k-off-diagonal estimates with r ∈ (1, 2]. These results when k := 1 and L := L1 are known.     

Weighted norm inequalities for the commutators of multilinear singular integral operators

In this paper, the authors consider the weighted estimates for the commutators of multilinear Calderón-Zygmund operators.By introducing an operator which shifts the commutation, and establishing the weighted estimates for this new operator, the authors prove that, if p₁ ∈ （1,∞）, p₂,…,p_m ∈(1,∞], p ∈ （0,∞） with 1/p =Σ1≤k≤ m 1/pk, then for any weight w, the commutators of m-linear Galderón-Zygmund operator are bounded from L^P1（Rⁿ,M_l（logL）^σw）× p2（Rn,M^w）×...×Lpm（Rn,Mw） to Lp（Rn,w）with σ to be a constant depending only on p₁ and the order of commutator     

A Class of Constrained Inverse Eigenproblem and Associated Approximation Problem for Symmetric Reflexive Matrices

Let S∈Rn×n be a symmetric and nontrival involution matrix. We say that A∈E R n×n is a symmetric reflexive matrix if AT = A and SAS = A. Let S R r n×n(S)={A|A= AT,A = SAS, A∈Rn×n}. This paper discusses the following two problems. The first one is as follows. Given Z∈Rn×m (m < n),∧= diag(λ1,...,λm)∈Rm×m, andα,β∈R withα<β. Find a subset (?)(Z,∧,α,β) of SRrn×n(S) such that AZ = Z∧holds for any A∈(?)(Z,∧,α,β) and the remaining eigenvaluesλm 1 ,...,λn of A are located in the interval [α,β], Moreover, for a given B∈Rn×n, the second problem is to find AB∈(?)(Z,∧,α,β) such that where ||.|| is the Frobenius norm. Using the properties of symmetric reflexive matrices, the two problems are essentially decomposed into the same kind of subproblems for two real symmetric matrices with smaller dimensions, and then the expressions of the general solution for the two problems are derived.     

LP[0,1](1＜p＜∞)空间正系数多项式倒数逼近的一个推广

本文推广了LP[0,1](1＜p＜∞)空间函数的正系数多项式的倒数逼近的结论,即证明了:设f(x)∈LP[0,1],1＜p＜∞,且在(0,1)内严格1次变号,则存在一点x0∈(0,1)及一个n次多项式Pn(x)∈∏n(+)使得‖f(x)-x-x0/Pn(x)‖LP[0,1]≤Cpω(f,n-1/2)LP[0,1],其中∏n(+)为次数不超过n的正系数多项式的全体.     

Multi-weight, Weighted Weak Type Estimates for the Multilinear Calderón-Zygmund Operators

Let m be an integer and T be an m-linear Calderón-Zygmund operator, u, v1,..., vm be weights. In this paper, the authors give some sufficient conditions on the weights (u, vk) with 1 ≤ k ≤ m, such that T is bounded from Lp1(Rn, v1) × ··· × Lpm(Rn, vm) to Lp,∞(Rn, u).     

Boundedness of singular integrals along surfaces on Lebesgue spaces

In the paper, we establish the Lp(Rn+1)-boundedness for a class of singular integral operators associated to surfaces of revolution {(y,γ(|y|),y ∈ Rn} with rough kernels. We also give several applications of this inequality.     

LP（Rn）-Boundedness of certain commutators

In this paper, the Lp(Rn)-boundedness of the commutators generalized by BMO(Rn) function and the singular integral operator T with rough kernel Ω∈ Llog+ L(Sn-1) is proved by using the Bony's formula for the paraproduct of two functions.     

沿旋转曲面奇异积分的有界性

本文建立了具有粗糙核的沿曲面奇异积分算子的L^P有界性．其中粗糙核K(y)=Ω（y)/|y|^n,y∈R^n以及曲面{(y，φ(|y|）)：y∈R^n)满足某种光滑条件．同时，相应极大算子的有界性也被得到.