Shepard-Lagrange算子的逼近

本文建立了Shepard-Lagrange算子逼近的正逆定理,证明了可以利用高阶光滑模来刻画Shepard-Lagrange算子的逼近性质.从而说明了Shepard-Lagrange算子比一般的Shepard算子具有更好的逼近性质.进一步,所用光滑模的阶梯函数非常广泛,这是多项式逼近所不具有的.     

球面卷积算子逼近

研究d维欧氏空间R~d中单位球面上卷积算子的逼近问题.利用球面乘子理论以及K-泛函与光滑模等价关系,建立一类球面卷积算子逼近的正、逆定理.特别地,给出了逼近的强型逆向不等式,从而揭示了该类球面卷积算子的本质逼近阶.此外,作为应用,给出了球面Jackson-Matsuoka卷积算子与Abel-Poisson卷积算子逼近上、下界的相同阶估计.     

用线性弱正算子逼近

用线性正算子的逼近理论飞速发展,但正性是一个较强的限制,孙永生,王仁宏等研究过减弱正性限制,作者研究用线性弱正算子逼近,推广Korovkin定理和Grundmann定理等等.     

Bernstein型算子同时逼近误差

该文证明了C[0,1]空间中的函数及其导数可以用Bernstein算子的线性组合同时逼近,得到逼近的正定理与逆定理.同时,也证明了Bernstein算子导数与函数光滑性之间的一个等价关系.该文所获结果沟通了Bernstein算子同时逼近的整体结果与经典的点态结果之间的关系.     

F格上的逼近算子

粗集理论是波兰学者Pawlak提出的知识表示新理论.Pawlak代数是粗集理论中粗集系统的抽象,其公理系统包含了知识粗表示所必须的全部性质.本文深入研究了F格上的逼近算子,建立了F格上弱逼近算子之间的某些代数运算,从而从理论上建立了各种知识粗表示之间的联系.我们还定义了逼近算子的闭包,进而用逼近算子导出拓扑,为信息系统的近似提供必要的数学基础.最后,作为特例,我们研究了粗集理论中由相似关系导出逼近算子的某些性质.     

m次积分余弦算子函数的逼近

m次积分余弦算子函数是近年来提出并研究的一类算子族,它的逼近问题是研究的课题之一.目的在于研究如何用生成元预解式的逼近来刻画m次积分余弦算子函数的逼近.利用Laplace变换得到了m次积分余弦算子函数逼近的四个等价条件.当m=0时即为经典的余弦算子函数相应的逼近结果.     

Cardaliguet-Eurrard型神经网络算子逼近

研究多维Cardaliguet-Eurrard型神经网络算子的逼近问题.分别给出该神经网络算子逼近连续函数与可导函数的速度估计,建立了Jackson型不等式.     

Bernstein 算子的同时逼近

借助于D itzian-T otik光滑模研究了Bernstein算子的同时逼近问题,给出了Bernstein算子同时逼近的正定理和等价定理.     

修正的q-Baskakov-Durrmeyer-Stancu算子的逼近性质

基于q-微积分的概念引入一类修正的Stancu型q-Baskakov-Durrmeyerr算子,并且借助连续模研究该算子的一些局部逼近性质,得到了算子的局部逼近定理.同时讨论的算子的加权逼近.     

一类Bernstein型算子加权逼近

本文首先给出了一类用递归法定义的Ｂｅｒｎｓｅｉｎ型算子在一致逼近意义下的特征刻划,然后指出在通常的加权范数下,它虹无界的,通过引入的一种新范数,我们给出了该算子加Ｊａｃｏｂｉ权逼近的特征刻划。     

白噪声分析中广义算子值函数的Bochner-Wick积分

白噪声广义算子在白噪声分析理论及其应用中起着十分重要的作用. 本文主要讨论了白噪声广义算子值函数的积分及相关问题. 主要工作有: 引入了广义算子值测度的概念, 分别讨论了这种测度在象征和算子p-范数意义下的变差及相互关系; 借助于广义算子的Wick积运算, 引入了广义算子值函数关于广义算子值测度的一种积分---Bochner-Wick积分, 讨论了这种积分的性质, 建立了相应的收敛定理并且展示了其在量子白噪声理论中的应用; 探讨了Bochner-Wick积分的Fubini定理及相关问题.     

复合算子和一类解析Toeplitz算子的约化子空间

本文利用复合算子完全刻画了符号为两个Ｂｌａｓｃｈｋｅ因子乘积的解析Ｔｏｅｐｌｉｔｚ算子的约化子空间。     

加权Bergman空间上Toeplitz算子的本质谱

本文探讨加权Bergman空间Ap(φ)上Toeplitz算子,刻画了L∞(D)的使得符号在其中的Toeplitz算子的半换位子是紧算子的最大的自伴子代数Q,并计算了符号在Q中的Toeplitz算子的本质谱和Fredholm指标．     

The Operator Valued Autoregressive Filter Problem and the Suboptimal Nehari Problem in Two Variables

Necessary and sufficient conditions are given for the solvability of the operator valued two-variable autoregressive filter problem. In addition, in the two variable suboptimal Nehari problem sufficient conditions are given for when a strictly contractive little Hankel has a strictly contractive symbol.     

The Foundamental Solution of Weighted Cauchy Problem for One-ordered Fuchsian Type Pseudodifferential Operator

In this paper, we begin with introducing two classes of generalized pseudo-homogeneous functions θ^m and T^m studying their basic properties. Then, under the most general hypothesis, we get the global foundamental solution of weighted Cauchy problem for one-order Fuchsian-typc pseudodifferential operator in the frame PsDO whose symbol belongs to C (D, S^m_{1,0}).     

Operator Frames for Banach Spaces

In this paper, operator Bessel sequences, operator frames, Banach operator frames, Operator Riesz bases for Banach spaces and dual frames of an operator frame are introduced and discussed. The necessary and sufficient condition for a Banach space to have an operator frame, a Banach operator frame or an operator Riesz basis are given. In addition, operator frames and operator Riesz bases are characterized by the analysis operator of operator Bessel sequences.     

非线性Lipschitz算子的Lipschitz对偶算子及其应用

在文山中我们对非线性Ｌｉｐｓｃｈｉｔｚ算子定义了其Ｌｉｐｓｃｈｉｔｚ对偶算子，并证明了任意非线性Ｌｉｐｓｃｈｉｔｚ算子的Ｌｉｐｓｃｈｉｔｚ对偶算子是一个定义在Ｌｉｐｓｃｈｉｔｚ对偶空间上的有界线性算子．本文还进一步证明：设Ｃ为 Ｂａｎａｃｈ空间 Ｘ的闭子集，Ｃ＊Ｌ为Ｃ的 Ｌｉｐｓｃｈｉｔｚ对偶空间，Ｕ为 Ｃ＊Ｌ上的有界线性算子，则当且仅当 Ｕ为 ｗ＊－ｗ＊连续的同态变换时，存在Ｌｉｐｓｃｈｉｔｚ连续算子Ｔ，使Ｕ为Ｔ的Ｌｉｐｓｃｈｉｔｚ对偶算子．这一结论的理论意义在于：它表明一个非线性Ｌｉｐｓｃｈｉｔｚ算子的可逆性问题可转化为有界线性算子的可逆性问题．作为应用，通过引入一个新概念──ＰＸ－对偶算子，在一般框架下给出了非线性算子半群的生成定理．     

Continuity of Pseudo-differential Operators Associated with the Bessel Operator in Some Gevrey Spaces

The pseudo-differential operator (p.d.o) h w , a associated with the Bessel operator d 2 / dx 2 + (1 m 4 w 2 )/4 x 2 involving the symbol a ( x , y ) whose derivatives satisfy certain growth conditions depending on some increasing sequences, is studied on certain Gevrey spaces (ultradifferentiable function spaces). It is shown that the operator h w , a is a continuous linear map of one Gevrey space into another Gevrey space. A special p.d.o. called the Gevrey-Hankel potential is defined and some of its properties are investigated. A variant H w , a of h w , a is also discussed.     

Operator norm localization property of metric spaces under finite decomposition complexity

The notions of operator norm localization property and finite decomposition complexity were recently introduced in metric geometry to study the coarse Novikov conjecture and the stable Borel conjecture. In this paper we show that a metric space X has weak finite decomposition complexity with respect to the operator norm localization property if and only if X itself has the operator norm localization property. It follows that any metric space with finite decomposition complexity has the operator norm localization property. In particular, we obtain an alternative way to prove a very recent result by E. Guentner, R. Tessera and G. Yu that all countable linear groups have the operator norm localization property.     

On the Algebra Generated by the Bergman Projection and a Shift Operator I

Let be a domain with smooth boundary and let α be a C ²- diffeomorphism on satisfying the Carleman condition .We denote by the C*-algebra generated by the Bergman projection of G, all multiplication operators aI and the operator where is the Jacobian of α. A symbol algebra of is determined and Fredholm conditions are given. We prove that the C*-algebra generated by the Bergman projection of the upper half-plane and the operator is isomorphic and isometric to . Submitted: February 11, 2001?Revised: January 27, 2002