多元Kantorovich算子的最优逼近类

本文研究定义在单纯形上的多元Kantorovich算子逼近的正逆不等式与饱和定理,给出该算子在Lp(1≤p≤∞)空间的最优逼近类,即利用K-泛函的特征刻画分别满足‖Knf-f‖p=O(n-1)与‖Knf-f‖p=o(n-1)的函数类.     

de Sitter空间中具有常数量曲率的完备类空子流形的间隙现象

设Mn是de Sitter空间Snp p(c)中具有常数量曲率R(≤c)的完备类空子流形.得到了Mn关于其第二基本形式模长平方‖h‖2的间隙性定理,如果n(c-R)≤‖h‖2≤2√n-1c,那么,或者‖h‖2=n(c-R)且Mn是全脐点子流形,或者‖h‖2=2√n-1c且Mn是全脐的或是双曲柱面Sn-1(c-tanh2r)×H1(c-coth2r).     

B值移动平均过程的Strassen重对数律

设 {ε,εt;t∈ Z}是 iid的 B值随机变量序列 ,{ aj;j∈ Z}是一个实数列 ,满足 ∞j=-∞|aj|<∞ .记 Xt= ∞j=-∞ajεt-j,Sn = nt=1Xt.对 p≥ 1 ,本文研究了n-1 -( p/ 2 ) (2 L2 n) -( p/ 2 ) ni=1 ‖ Si‖p 及 n-1 -( p/ 2 ) (2 L2 n) -( p/ 2 ) ni=0 ‖ Sn- Si‖ p的渐进性质 ,使得 Strassen(1 964)及 Chen(1 994)的一些结果得到推广 .     

Fourier-Laplace级数的强逼近

设f是Rn(n≥3)中单位球面∑n-1上的可积函数,Sθ(f)是步长为θ∈R的平移算子.σδN(f)是Fourier-Laplace级数的δ阶Ceaaro平均.如果∫π0 |Sθ(f)-f|p/θ2dθ∈ L∞ (∑n- 1 ),则∑∞k=0 |σλk(f)-f|p∈L∞(∑n-1)且∑∞k=0(f)-f|p∈L∞(∑n-1 ),其中Eλk(f)为Cesaro平均σλk的等收敛算子.     

L~(p(x))(Ω)中关于Luxemburg范数和共轭Orlicz范数间的一个最佳不等式

令 L~(p(x))(Ω)为变指数 Lebesgue空间,其中 p：Ω→[1,∞]．‖·‖_(p(x))和‖·‖_(p(x))~o 分别表示 L~(p(x))(Ω)中的 Luxemburg 范数和共轭 Orlicz 范数．本文证明成立最佳不等式‖·‖_(p(x))≤‖·‖_(p(x))~o ≤ d_(p-,p )‖·‖_(p(x)),其中 d_(p-,p )是一个依赖于 p-=essinf_Ωp(x)和 p =esssup_Ωp(x)的常数．当1＜p-＜p ＜∞时, (?) 当 p-=1或 p =∞时,d(p-,p )是相应的极限形式．     

B值鞅的强大数定律

本文证明了在 p 阶光滑空间中的 B 值鞅差序列{D_n},若存在 q≥1及递增的正实数列{a_n},a_n↑∝(n→∝),满足sum from n=1 to ∞ a_n~(-p)(a_n~p-a_(n-1)~p)~(-(q-1))E‖D_n‖~(pq)<∝ (a_0=0)则(sum from i=1 to n D_i)/a_n→0 a.s.(n→∝)并得到了 p 阶光滑空间特征的两个新刻划,应用到其它几种 B 值鞅型序列,也获得一些结果。     

一类共振条件下的高阶p-Laplacian算子多点边值问题

主要讨论了下列n阶带p-Laplacian算子多点边值问题在共振条件下解的存在性.(Φp(x(n-1)))′+f(t,x,x′,…,x(n-2))=0,0相似文献   

COEFFICIENT MULTIPLIERS ON MIXED NORM SPACES

§1　IntroductionSuppose thatf is analytic in the open unit disc D in the complex plane.We defineMp(r,f) =12π∫2π0 | f(reiθ) | pdθ1 / p,0

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代数Paranormal算子的谱

若任给x∈H,‖Tx‖~2≤‖T~2x‖·‖x‖,T∈B(H)称为是一个paranormal算子.T∈B(H)称为代数paranormal算子,若存在非常值复值多项式p,使得p(T)为para- normal算子.本文利用代数paranormal算子的谱集的特点,研究了代数paranormal算子以及该算子的拟仿射变换的Weyl型定理.     

关于B值随机元赋范部分和最大值的矩的若干讨论

本文讨论B值随机元部分和序列的最大值的矩的问题,对1≤p≤2及r>p证明了下列叙述的等价性; (ⅰ)存在常数0相似文献   

A note on Weyl's theorem

The Kato spectrum of an operator is deployed to give necessary and sufficient conditions for Browder's theorem to hold.

     

建立在L-凸空间上的截口定理及其应用

In this paper,the author gives a new section theorem in L-convex spaces.And as its applications,the author proves a coincident theorem and a two-functional minimax theorem established in L-convex spaces.     

Weyl type theorems and hypercyclic operators II

In this note, the relation between hypercyclic operator matrices (or supercyclic operator matrices) and the operator matrices which satisfy Weyl type theorems is discussed. Also, using a variant of the essential approximate point spectrum, we give the necessary and sufficient conditions for for which a-Browder's theorem or a-Weyl's theorem holds.

     

The Additivity Theorem in K-Theory

We present a method for converting Theorem B style proofs in algebraic K-theory to Theorem A style proofs and apply it to the additivity theorem.     

Drazin谱和算子矩阵的Weyl定理

A∈B(H)称为是一个Drazin可逆的算子,若A有有限的升标和降标．用σ_D(A)={λ∈C：A-λI不是Drazin可逆的)表示Drazin谱集．本文证明了对于Hilbert空间上的一个2×2上三角算子矩阵M_C=■,从σ_D(A)∪σ_D(G)到σ_D(M_C)的道路需要从前面子集中移动σ_D(A)∩σ_D(B)中一定的开子集,即有等式：σ_D(A)∪σ_D(B)=σ_D(M_C)∪G,其中G为σ_D(M_C)中一定空洞的并,并且为σ_D(A)∪σ_D(B)的子集．2×2算子矩阵不一定满足Weyl定理,利用Drazin谱,我们研究了2×2上三角算子矩阵的Weyl定理,Browder定理,a-Weyl定理和a-Browder定理．     

Some compactness theorems via m-Bakry–Émery and m-modified Ricci curvatures with negative m

Stimulated by S. Ohta and W. Wylie, we establish some compactness theorems for complete Riemannian manifolds via m-Bakry–Émery and m-modified Ricci curvatures with negative m. Our results may be considered as generalizations of the classical compactness theorems via Ricci curvature due to S.B. Myers, W. Ambrose, G.J. Galloway, and J. Cheeger, M. Gromov, and M. Taylor, and relax some previous compactness criteria for complete Riemannian manifolds via m-Bakry–Émery and m-modified Ricci curvatures obtained when m is a positive constant or infinity.     

Multipermutation-Based Intersection Theorem and Its Applications

In this paper, we introduce a multipermutation-based intersection theorem on the product space of several unit simplices, called the simplotope. This theorem gives a substantial generalization of an intersection result of Scarf on the unit simplex (Ref. 1). By using this new result, we also obtain a multipermutation-based generalization of the Brouwer fixed-point theorem on the simplotope. Furthermore, we apply this new result to an economic equilibrium model with indivisibilities and obtain an equilibrium existence theorem.     

The affine separation problem revisited

The aim of this note is to characterize in terms of inequalities those pairs of real functions (acting on a convex subset of a vector space) that possess an affine separator. The main result is originally due to Behrends and Nikodem. Their method is based on the Hahn–Banach Theorem and a variant of the Helly Theorem. In our approach, a direct and independent proof is presented via the Radon and the Helly Theorems.     

A note on the colorful fractional Helly theorem

Helly’s theorem is a classical result concerning the intersection patterns of convex sets in ${\mathbb{R}}^d$. Two important generalizations are the colorful version and the fractional version. Recently, Bárány et al. combined the two, obtaining a colorful fractional Helly theorem. In this paper, we give an improved version of their result.