某些指数型算子在多项式权空间的整体逼近定理  

Global Approximation Theorems for Some Exponential-type Operators in Polynomial Weight Spaces

作　　者：陈文忠[1] 古四毛[1] 

机构地区：[1]厦门大学

出　　处：《工程数学学报》1992年第4期67-75,共9页Chinese Journal of Engineering Mathematics

基　　金：福建省自然科学基金

摘　　要：本文统一地建立了一类指数型算子在多项式权空间的整体逼近正定理及逆定理。Let I=[0,∞), the sequence {λ_(nx)(x)}_(k=0)~∞ is called an exponential-type kernal on I and denoted by {λ_(nx)(x)}_(k=0)~∞∈E_β, if it satisfies the folllowing condition,i) For x∈I^0, λ_(n,k)(x)>0(0≤k<∞) and where I^0 is the interior of Iii) λ_(n,k)(x)∈C∞(I) (0≤k<∞) and satisfiesx(1+βx)λ_(n,k)(x)=(k-nx)λ_(n,k)(x)where β≥0.We consider spaces C_N defined via the weight W_N(x) as follows (N∈P, P=NU{0}), W_0(x)=1. W_N(x)=(1+x^N)^(-1)(x≥0, n∈N), C_N={f∈C[0,∞); W_funiformly continuous and bounded on [0,∞)} The corresponding Lipschitz classes are given for 0<α≤2 by (h>0) Then we have the following results,Theorem Let N∈P, α∈(0,2), f∈C_N, {λ_(nk)(x)∈E_β, Then theapproximation rate is equivalent to f∈Lip_N^2α, where the constants M_Nare independent of n and x.

关 键 词：算子 指数型 多项式权空间 逼近 

分 类 号：O174.41[理学—数学]