BEST SIMULTANEOUS Lp APPROXIMATION

In this paper we discuss the exigtenoe of best simultaneous L_p approximation and give the characterization theorems of best simultaneous L_p approximation using the elements of an arbitrary quasioonvex set K in the space \[{L_p}(X,\sum ,\mu )\], A set \[K \subset {L_p}(X,\sum ,\mu )\] is called quasiconvex if for arbitrary elements \[{h_1},{h_2} \in K\] there exists a sequenoe \[{t_n} > 0\] (n = l, 2, ...), \[{t_n} > 0\]->0 (n—>∞) such that \[{t_n}{h_1} + (1 - {t_n}){h_2} \in \bar K(n = 1,2,...)\] where \[{\bar K}\] denotes a closure of K.     

Hqp(01)空间中的多项式最佳逼近问题

In this paper, we obtained two direct theorems and a inverse theorem on the best approximation by polynomials in H_q^p(01) spaces. The results obtained in this paper are just some direct extensions from the case p= 1 to the case 0相似文献   

APPROXIMATION ORDER AND INTERPOLATION SPACES

In this paper we introduce the two-parameter operators on Abelian group and establish their interpolation theorems of approximation, which are extensions of the interpolation theorems for nonlinear best approximation by R. Devore and are suitable for the approximation of oprators.     

关于FA,δ—环与广义周期环的几个定理

In this paper,we introduced the concept of F_A,δ-ring and the concept of generalized periodic ring, the structure theorems for some F_A,δ-rings and generalized periodic rings are given.     

某些空间的等距算子

In this paper , We give some representation theorems of isometrics of (L^p₁∩L^p₂(012<+∞), and aslo, obtain some representations of some isometries of L^p(μ,E)(0相似文献   

关于拟微分算子有界性定理的改进形式

Calderon A. P. et al. were studied a class of the bounded pseudo-differential-operators of order -M and type ρ,δ₁, δ₂, and showed them to be bounded in L² provided that 0≤ρ≤δ₁<1, 0≤ρ≤δ₂<1 and M/n≥1/2(δ₁+δ₂)-ρ. H?raander et al. have shown that if the aforecited conditions are not valid, then the conclusion that A is bounded in L² isn't necessarily right. Calderon et al. settled the borderline case and remove the restriction on the support of a.     

Sample Numbers and Optimal Lagrange Interpolation of Sobolev Spaces Wr1*

This paper investigates the optimal recovery of Sobolev spaces W^r₁[?1, 1], r ∈ N in the space L1[?1, 1]. They obtain the values of the sampling numbers of W^r₁[?1, 1] in L₁[?1, 1] and show that the Lagrange interpolation algorithms based on the extreme points of Chebyshev polynomials are optimal algorithms. Meanwhile, they prove that the extreme points of Chebyshev polynomials are optimal Lagrange interpolation nodes.     

用Hermite-Fejér型插值多项式逼近连续函数

Let f(x)∈C_[-1,1],T_n(x)=cos (n arccos x),U_n(x)=(sin((n+1)arccosx))/(1-x²)^1/2,P_n(x) be the Legendre polynomials of degree n. And let ω(t ) be a given modulus of continuity, H_ω={f|ω(f,t)≤ω(t)}.A. K. Sharma and J. Tzimbalario(J. Appro. Th., 13(1975), 431-442) considered the operators L_n,p (f, x) (p= 0, 1, 2,3) and obtained some theorems.In this paper, we prove the following theorems.     

E1类中多项式和有理函数的最佳逼近

In this paper we obtain some estimations of the degree of the best approximation in E¹ space of functions by polynomials and rational functions with preas-signed poles, in which D is an Альпер region, its boundary p satisfies the condition ∫₀(j(u))/u|lnu|du<∞, where j(u) is the continuous modulus of the angle between the tangent of Γ and the positive real axis as the function of the arc length of Γ.     

球面Schr?dinger算子的迹

Let S be a unit sphere in R³,Δ_θ,φ be the spherical Laplasian and q(θ,φ) be a continuous function on S. The following trace formulae are proved for the eigenvalues μ_n of L₀=-Δ_θ,φ and λ_n of L=L₀+q.