摘要
本文对广义指数型算子建立算子导数的渐近阶与函数光滑模之间的等价关系,这个命题是Z.Ditzian首先提出的。
Let U=[0,1]or [0,∞), I0denotes the inner kernel of I, and φ(x)= x(1+αx)>0(x ∈ I0), here α=-1 or α≥0.Also, n+ denotes n or +∞. Suppoes and , and satisfies thefollowing equation:Now, for f ∈ C(I) we define the following positive linear operators, which are called the generalized exponential type operators.where φ(f) =f(k/n) (0≤k≤n+) or φ(?)(f)=f(0) and In this parper, the equivalence relations between the asymptotic behaviour of derivative of the generalized exponential type operator and the smoothness of the function they approximate are given. We haveTheorem. Let (no matter how small η>0 is). Then, for0<β≤r,ωr(f,h)≤M2hβ(r=1,2)iff
出处
《厦门大学学报（自然科学版）》
CAS
CSCD
北大核心
1989年第1期12-18,共7页
Journal of Xiamen University：Natural Science
基金
福建省自然科学基金
关键词
指数型算子
算子导数
光滑模
Generalized exponential type operator, Smoothness, Asymptotic behaviour, Derivative of the operator
