复赋范空间中复RS集的最佳同时逼近

研究了复赋范空间中具限制系数的广义多项式集G对无穷序列的最佳同时逼近问题,得到了特征定理;当G是复RS集时还得到了惟一性定理．     

Banach空间中太阳集对无穷序列的最佳同时逼近

本文研究太阳集对一列无穷序列的最佳同时逼近问题，建立了特征及唯一性结果．     

赋范线性空间中同时远达点的唯一性

1 引言 设X为一实赋范线性空间,给定X中的子集G和有界子集K,令(?)和C分别表示X的所有非空有界子集与相对紧子集的全体,对A∈B,记 若x_(0)∈K满足sup||a-x_(0)||=Fk(A),则称x_(0)是A关于K的同时远达点,A关于K的同时远达点的全体记为Q_(K)(A),即     

关于“线性赋范空间联合最佳逼近的特征”一文的一点评注

在线性赋范空间X中,一个凸子集G对点列{x_n}的联合最佳逼近的特征,[1]中给出了泛函形式及变分形式的两条定理,即定理3.2及3.3. 通常与p有关的最佳逼近的特征,p=1与p>1应有不同的变分形式.众所周知,函数空间L~p(T,μ)(P≥1)内最佳逼近的特征就是如此.但定理3.3对p=1与p>1     

赋范线性空间的限制逼近及其应用

这里A是某个紧Hausdorff空间,l,u∈C(A).G是由{h_1,…,h_n}张成的n维子空间,且满足下述条件: i)h_i是定义在T∪A上的函数,且在T上,h_i∈L_p~w(T,μ),在A上连续(i=1,2,…,n)。 ii){h_i}_i~n=1在T和A上分别是线性无关的.     

赋范线性空间中的最佳共逼近的一点注记

本文用例子表明最佳共逼近与最佳逼近间有着区别．指出强共逼近的元未必是唯一的;凸集未必是共太阳集和强共Ｋｏｌｍｏｇｏｒｏｖ集;而在最佳逼近论中它们的相应回答均是肯定的．     

关于随机赋范模中最佳逼近的一个注记

证明了随机赋范模中一个点是其任一子模的依概率范数的弱最佳逼近点当且仅当它是该子模的依概率范数的最佳逼近点,亦当且仅当该点是该子模的依随机范数的最佳逼近点.利用这些关系我们可以借助于随机赋范模的最近进展获得许多概率赋范空间中的新的最佳逼近定理.     

Lp（T,X）内太阳集的逼近性质

设（Ｔ，Σ，ｕ）是有限测定空间，表示定义在Ｔ上取值于Ｘ的ｐ幂Ｂｏｃｈｎｅｒ可积函数空间。本文主要证明了Ｌｐ（Ｔ，Ｘ）中的一般子集Ｇ和Ｌｐ（Ｔ，Ｙ）型子集为太阳集的特征定理；对实Ｈｉｂｅｒｔ空间Ｘ，得到了子集Ｌｐ（Ｔ，Ｙ）为Ｌｐ（Ｔ，Ｘ）的半Ｃｈｅｂｙｓｈｅｖ太阳集的特征，同时给出了子集Ｌｐ（Ｎ，Ｙ）是Ｌｐ（Ｎ，Ｘ）的强Ｃｈｅｂｙｓｈｅｖ子空间的条件。     

On the Best Approximation in Non-Archimedean Normed Linear Spaces

ＯｎｔｈｅＢｅｓｔＡｐｐｒｏｘｉｍａｔｉｏｎｉｎＮｏｎ－ＡｒｃｈｉｍｅｄｅａｎＮｏｒｍｅｄＬｉｎｅａｒＳｐａｃｅｓｏｎＷｅｉｄｕｎ（邱维敦）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＬｏｎｇｙｏｎＮｏｒｍａｌＣｏｌｌｅｇｅ，Ｆｕｊｉａｎ，３６...     

On Best Approximations from RS-sets in Complex Banach Spaces

The concept of an RS-set in a complex Banach space is introduced and the problem of best approximation from an RS-set in a complex space is investigated. Results consisting of characterizations, uniqueness and strong uniqueness are established,     

Weak Type Inequalities for Best Simultaneous Approximation in Banach Spaces

For arbitrary Banach spaces Butzer and Scherer in 1968 showed that the approximation order of best approximation can characterized by the order of certain K-functionals. This general theorem has many applications such as the characterization of the best approximation of algebraic polynomials by moduli of smoothness involving the Legendre, Chebyshev, or more general the Jacobi transform. In this paper we introduce a family of seminorms on the underlying approximation space which leads to a generalization of the Butzer–Scherer theorems. Now the characterization of the weighted best algebraic approximation in terms of the so-called main part modulus of Ditzian and Totik is included in our frame as another particular application. The goal of the paper is to show that for the characterization of the orders of best approximation, simultaneous approximation (in different spaces), reduction theorems, and K-functionals one has (essentially) only to verify three types of inequalities, namely inequalities of Jackson-, Bernstein-type and an equivalence condition which guarantees the equivalence of the seminorm and the underlying norm on certain subspaces. All the results are given in weak-type estimates for almost arbitrary approximation orders, the proofs use only functional analytic methods.     

Best Local Approximation in Orlicz Spaces

We get results in Orlicz spaces L ^φ about best local approximation on non-balanced neighborhoods when φ satisfies a certain asymptotic condition. This fact generalizes known previous results in L ^p spaces.     

置换空间中的最佳逼近

我们首次得到了置换空间PXXn中的点到太阳集的最佳逼近特征定理.     

赋Amemiya-Orlicz范数的Musielak-Orlicz-Sobolev空间单调性在最佳逼近中的应用

利用Musielak-Orlicz-Sobolev空间的构成特点,借鉴Orlicz-Sobolev空间的单调性在最佳逼近中的一些应用,以Orlicz空间中Jensen'S不等式的推广为主要工具,讨论了赋Amemiya-Orlicz范数的Musielak-Orlicz-Sobolev空间中的最佳逼近问题,主要是唯一性、存在性、稳定性.     

Best Interpolatory Approximation in Normed Linear Spaces

A theory of best approximation with interpolatory contraints from a finite-dimensional subspaceMof a normed linear spaceXis developed. In particular, to eachxX, best approximations are sought from a subsetM(x) ofMwhichdependson the elementxbeing approximated. It is shown that this “parametric approximation” problem can be essentially reduced to the “usual” one involving a certainfixedsubspaceM₀ofM. More detailed results can be obtained when (1) Xis a Hilbert space, or (2) Mis an “interpolating subspace” ofX(in the sense of [1]).     

Best N Term Approximation Spaces for Tensor Product Wavelet Bases

We consider best N term approximation using anisotropic tensor product wavelet bases ("sparse grids"). We introduce a tensor product structure ⊗_q on certain quasi-Banach spaces. We prove that the approximation spaces A^α_q(L₂) and A^α_q(H¹) equal tensor products of Besov spaces B^α_q(L_q), e.g., A^α_q(L₂([0,1]^d)) = B^α_q(L_q([0,1])) ⊗_q · ⊗_q B^α_{q · ·}(L_q([0,1])). Solutions to elliptic partial differential equations on polygonal/polyhedral domains belong to these new scales of Besov spaces.