变量核奇异积分和分数次微分加权范不等式

用T和D~γ(0≤γ≤1)分别表示变量核奇异积分和分数次微分算子.T~*和T~#分别为T的共轭算子及拟共轭算子.利用球调和多项式展式,本文得到了TD~γ-D~γT和(T~*-T~#)D~γ在B_ω~(q,λ)(R~n)上的有界性.同时也得到了变量核奇异积分的积T_1T_2和拟积T_1■T_2的加权范不等式.     

一类奇异积分算子在加权空间的界的估计

设T是由Grubb和Moore引入的一类奇异积分算子,它的核满足一种新型利普希茨正则性.T^*是由T确定的极大奇异积分算子.本文通过建立与T和T^*相关的grand极大算子的弱型端点估计,得到了算子T和T^*在加权空间的由A_p权常数表示的界的估计和弱型端点估计.     

极分解定理的注记

设H和K是Hilbert空间.首先,对给定的算子T∈B（H,K）,刻画了集合U_T={U∈B（H,K）：U是部分等距算子并且T=U（T^*T）^1/2}. 其次,对部分等距算子U∈B（H,K）,还给出集合T_U={T∈B（H,K）：N（T）=N（U）,R（T）=R（U）,T=U（T^*T）^1/2}的刻画. 最后,作为主要结果的应用得到了相关结论.     

拟-*-A(n)算子的谱性质

我们证明了以下结论:(1)若T是拟-*-A(n)算子,则T是似正规算子.(2)若E是拟-*-A(n)算子T的非零孤立谱点λ的Riesz幂等算子,则E是自共轭的且满足R(E)=N(T-λ)=N(T-λ)*.(3)若T或T^*是代数拟-*-A(n)算子,则f(T)满足Weyl定理.(4)若T*是代数拟-*-A(n)算子,则f(T)满足Weyl定理.(4)若T^*是代数拟-*-A(n)算子,则f(T)满足α-Weyl定理,其中f∈H(σ(T)).     

一类具有内部奇异点的微分算式乘积的自伴域

本文研究一类带有内部奇异点的n阶复值系数对称微分算式ty=Σna_j（t）y^（j）（t）乘积的自共轭域描述问题.通过构造相应的直和空间,应用直和空间的相关理论,在直和空间上生成的相应于l的最小算子T₀（l）的正则型域Π（T₀（l））满足（-r,r）■Π（T₀（l））∩R及l²在直和空间中是部分分离的条件下,利用微分方程ly=±λy的解给出l²的自共轭域的完全解析描述,并且确定自共轭边界条件的矩阵仅由微分方程的解在正则点的初始值决定,其中0相似文献   

k-拟-*-A(ｎ)算子的性质(英文)

An operator T is called k-quasi-*-A（n） operator, if T^*k|T¹⁺ⁿ|^2/（1+n）T^k ≥T^*k|T^* |²T^k , k ∈ Z, which is a generalization of quasi-*-A（n） operator. In this paper we prove some properties of k-quasi-*-A（n） operator, such as, if T is a k-quasi-*-A（n） operator and N（T ）■N（T^* ）, then its point spectrum and joint point spectrum are identical. Using these results, we also prove that if T is a k-quasi-*-A（n） operator and N（T ）■N（T ）, then the spectral mapping theorem holds for the Weyl spectrum and for the essential approximate point spectrum.     

On Two Natural Extensions of n-normality

A bounded linear operator T on a complex Hilbert space H is called n-normal if T^*Tⁿ=TⁿT^*.By Fuglede’s theorem T is n-normal if and only if Tⁿ is normal.Let k,n∈ N.Then a bounded linear operator T is said to be of type Ⅰ k-quasi-n-normal if T^*k{T^*Tⁿ-TⁿT^*}T^k=0,and T is said to be of type Ⅱ k-quasi-n-normal if T^*k{T^*nTⁿ-TⁿT^*n...     

二维Hardy空间维林肯型系统的极大算子（英文）

本文研究二维Hardy空间维林肯型系统的极大算子的有界性.利用原子分解方法,我们证明二维极大算子T_αf:=sup₍2^-α≤n/m≤2^α)|f*P_n,m|是从鞅Hardy空间H^p到L^p有界的,其中0 *f=₍2^-α≤n/m≤2^α)|σ_n,mf|/([(n+1)(m+1)])^1/p-2的有界性证明.通过构造反例,我们证明二维极大算子■不是从鞅Hardr空间H^p到L^p有界的,其中0

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奇异摄动问题在Bakhvalov-Shishkin 网格上的流线扩散有限元逼近

本文采用线性插值的流线扩散有限元在Bakhvalov-Shishkin网格上求解一维对流扩散型的奇异摄动问题. 在ε ≤ N^-1的前提下,可以得到,关于扰动参数ε 是一致收敛的. 在离散的SD范数下,其u-u_I的误差阶提高到N^-2,u-u_h的误差阶达到N^-2（lnN）^0.5. 最后,通过数值算例,验证了理论分析.     

Hardy型算子在径向——角向混合空间上的最佳界（英文）

本文运用旋转方法算出了n维Hardy算子H在径向—角向混合空间上的最佳界.进一步,当0<ββ从L_|x|^p L_θ^p(Rⁿ)到L_|x|qL_θ^q(Rⁿ)上的最佳界.通过对偶建立了共轭算子H^*和H_β^*的相应结果.此外,还考虑了算子H的最佳弱型估计.     

A Bishop–Phelps–Bollobás Theorem for Asplund Operators

By characterizing Asplund operators through Fréchet differentiability property of convex functions, we show the following Bishop–Phelps–Bollobás theorem: Suppose that X is a Banach space,T : X → C(K) is an Asplund operator with ║T║= 1, and that x_0 ∈ S_X, 0 ε satisfy ║T(x_0)║ 1-ε~2/2.Then there exist x_ε∈ S_X and an Asplund operator S : X → C(K) of norm one so that ║S(x_ε)║ = 1, x_0-x_ε ε and ║T-S║ ε.Making use of this theorem, we further show a dual version of Bishop–Phelps–Bollobás property for a strong Radon–Nikodym operator T : ?_1 → Y of norm one: Suppose that y_0~*∈ S_(Y~*), ε≥ 0 satisfy T~*(y_0~*) 1-ε~2/2. Then there exist y_ε~*∈ S_(Y~*), x_ε∈(±e_n), y_ε∈ S_Y, and a strong Radon–Nikodym operator S : ?_1 → Y of norm one so that (ⅰ)║S(x_ε)║= 1;(ⅱ) S(x_ε) = y_ε;(ⅲ)║T-S║ ε;(ⅳ)║S~*(y_ε~*)║=y_ε~*, y_ε= 1;(ⅴ)║y_0~*-y_ε~*║ ε and (ⅵ)║T~*-S~*║ ε,where(e_n) denotes the standard unit vector basis of ?_1.     

Context-free grammars for triangular arrays

We consider context-free grammars of the form G = {f → fb1+b2+1ga1+a2, g → fb1 ga1+1},where ai and bi are integers sub ject to certain positivity conditions. Such a grammar G gives rise to triangular arrays {T(n, k)}0≤k≤n satisfying a three-term recurrence relation. Many combinatorial sequences can be generated in this way. Let Tn (x) =∑nk=0T(n, k)xk. Based on the differential operator with respect to G, we define a sequence of linear operators Pn such that Tn+1(x) = Pn(Tn(x)). Applying the characterization of real stability preserving linear operators on the multivariate polynomials due to Borcea and Br?ndén, we obtain a necessary and sufficient condition for the operator Pn to be real stability preserving for any n. As a consequence, we are led to a sufficient condition for the real-rootedness of the polynomials defined by certain triangular arrays, obtained by Wang and Yeh.Moreover, as special cases we obtain grammars that lead to identities involving the Whitney numbers and the Bessel numbers.     

Sampling from a Mixture of Different Groups of Coupons

A collector samples coupons with replacement from a pool containing g uniform groups of coupons, where "uniform group" means that all coupons in the group are equally likely to occur (while coupons of different groups have different probabilities to occur). For each j=1,..., g, let T_j be the number of trials needed to detect Group j, namely to collect all M_j coupons belonging to it at least once. We first derive formulas for the probabilities P {T₁ < … < T_g} and P {T₁=Λ_j=1^g T_j}. After that, without severe loss of generality, we restrict ourselves to the case g=2 and compute the asymptotics of P {T₁ < T₂} as the number of coupons grows to infinity in a certain manner. Then, we focus on T:=T₁ ∨ T₂, i.e. the number of trials needed to collect all coupons of the pool (at least once), and determine the asymptotics of E[T] and V[T], as well as the limiting distribution of T (appropriately normalized) as the number of coupons becomes large.     

带多项式相位的高维振荡积分算子的有界性

考虑如下的振荡积分算子:T_(m,k,n)f(x):=∫_(R~n)e~(i(x_1~2+…+x_n~2))~m(y_1~2+…+y_n~2)~kf(y)dy,其中函数f为定义在R~n上的Schwartz函数,并且满足m,k0.本文给出算子T_(m,k,n).从L~p(R~n)(1≤p∞)到L~q(R~n)有界的一个充分必要条件.此外,我们还证明了算子T_(m,k,n)把L~1(R~n)映到C_0(R~n).     

Multiple Positive Solutions for a Nonlinear Elliptic Equation Involving Hardy–Sobolev–Maz'ya Term

In this paper, we study the existence and nonexistence of multiple positive solutions for the following problem involving Hardy–Sobolev–Maz'ya term:-Δu- λu/|y|2=|u|pt-1u/|y|t+ μf(x), x ∈Ω,where Ω is a bounded domain in RN(N ≥ 2), 0 ∈Ω, x =(y, z) ∈ Rk× RN-kand pt =N +2-2t N-2(0 ≤ t ≤2). For f(x) ∈ C1(Ω)\{0}, we show that there exists a constant μ* 0 such that the problem possessesat least two positive solutions if μ∈(0, μ*) and at least one positive solution if μ = μ*. Furthermore,there are no positive solutions if μ∈(μ*, +∞).     

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).     

-manifolds and coassociative torus fibration

Let (?₀,g₀) be a flat G₂-structure on the torus T⁷ . For a certain finite group ?-action on T⁷ preserving the G₂-structure, Joyce constructed aclosed G₂-manifold M from the resolution of the orbifold T⁷/?. The main purpose of this paper is to prove that there exist global coassociative fibrations on open submanifolds of certain Joyce manifolds.     

重调和Hardy空间Toeplitz算子的交换性

本文研究重调和Hardy空间h~2(Ω)上,Toeplitz算子的交换性,给出了h~2(T~2)上一个解析Toeplitz算子与另一个共轭解析Toeplitz算子交换的充分必要条件.