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刘永平 《数学年刊A辑(中文版)》1992,(5)
本文研究了n-维立方体T_n上的符号测度和某些多变量函数通过它们的Bochner-Riesz球形平均S_R~a在全测度集上的逼近问题,并且得到两个主要定理。此外,作为单变量周期有界变差函数通过它们的Vallce-Poission平均,在全测度上逼近问题推广到n-维情形,可以从本文的结果导出。 相似文献
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Average Width and Optimal Recovery of Some Anisotropic Classes of Smooth Functions Defined on the Euclidean Space R~d 总被引:1,自引:0,他引:1
§ 1.Introduction and Main Results In[1 ] ,[2 ] ,the authors studied some problems of optimal recovery of functions de-fined on a cube,for a class of functions with partial derivatives of a fixed order havingmoduli of continuity not exceeding a given modules of continuity,and for the unit ballsSHαp in the spaces Hαp satisfying the mixed Holder conditionα,respectively.They ob-tained some weak asymptotic results. In[3 ] ,[4 ] and[5] ,Magarill-Il' yaev,Liu and Sun studied some proble… 相似文献
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讨论了以第二类Tchebycheff多项式的零点为插值结点组的Grünwald插值于Lp下的收敛性.当1≤p<2时,给出了收敛速度的一个精确估计;当p≥2时,说明了其Lp下不是收敛算子列.给出了一种以第二类Tchebycheff多项式的零点为插值结点组的修改的Grünwald插值,证明了其于Lp(1≤p<∞)下是收敛的. 相似文献
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We consider Jackson inequality in L~2(B~d × T,W_(κ,μ)~B(x)),where the weight function W_(κ,μ)~B(x) is defined on the ball B~d and related to reflection group,and obtain the sharp Jackson inequality E_(n- 1,m-1)(f)2 ≤k_(n,m)(r,r)ω_r(f,t)_2,T ≥ 2τ_(n,λ),where τ_(n,λ) is the first positive zero of the Gegenbauer cosine polynomial C_n~λ(cosθ)(n ∈ N). 相似文献
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我们研究了由仅有实零点的代数多项式导出的微分算子确定的广义Sobolev类利用指数型整函数作为逼近工具的最佳限制逼近问题.利用Fourier变换和周期化等方法,得到在L_2(R)范数下的广义Sobolev光滑函数类的相对平均宽度和最佳限制逼近的精确常数,以及当0是这个代数多项式的一个至多2重的零点时,得到最佳限制逼近在L_1(R)范数和一致范数下的广义Sobolev类的精确到阶的结果. 相似文献
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本文研究了极性基团浓度、碱金属盐阳离子和阴离子尺寸对均聚物聚环氧氯丙烷(PECH)和共聚物聚环氧氯丙烷-聚环氧乙烷(PECH-PEO)电导率的影响。对锂盐络合物,极性基团浓度增高,电导率降低。钠盐络合物则正好相反,极性基团浓度越高,电导率越高。碱金属盐阳离子和阴离子尺寸对聚合物离子导体电导率都有明显影响。所研究的聚环氧氯丙烷与三种碱金属盐络合物PECH-MI(M=Li,Na,K)的电导率数据表明,钠盐络合物的电导率最高,锂盐和钾盐络合物的电导率较低。碱金属盐阴离子越大,PECH络合物的电导率越低。此外,还
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We constructed a kind of continuous multivariate spline operators as the approximation tools of the multivariate functions on the Bd instead of the usual multivariate cardinal interpolation oper-ators of splines, and obtained the approximation error by this kind of spline operators. Meantime, by the results, we also obtained that the spaces of multivariate polynomial splines are weakly asymptoti-cally optimal for the Kolmogorov widths and the linear widths of some anisotropic Sobolev classes of smooth functions on Bd in the metric Lp(Bd). 相似文献
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This paper investigates the optimal Birkhoff interpolation and Birkhoff numbers of some function spaces in space L∞[-1,1] and weighted spaces Lp,ω[-1,1],1≤p<∞,with w being a continuous integrable weight function in(-1,1).We proved that the Lagrange interpolation algorithms based on the zeros of some polynomials are optimal.We also show that the Lagrange interpolation algorithms based on the zeros of some polynomials are optimal when the function values of the two endpoin... 相似文献
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