代数多项式和指数型整函数在Besov空间中的逼近

用Ｋ－泛函定义了一类Ｂｅｓｏｖ空间,并分别用ｎ阶代数多项式及指数为σ的整函数的最佳逼近阶给出了其特征的刻画。     

Approximation by rational functions with polynomials of positive coefficients as the denominators

The present paper proves that if f(x) ∈ C[0,1], changes its sign exactly l times at 0 ＜ y1 ＜ y2 ＜y1＜1 in(0,1),then there exists a pn (x)пn( ),such that |f(x)-p(x)/pn(x)|≤ Cωφ(f,n-1/2),where ρ(x) is defined by ρ(x)=l∏i=1(x - yi), if f(x) ≥ 0 for x ∈ (yl, 1),-1∏i=1(x-yi), iff(x) ＜ 0 for x ∈ (y1,1).which improves and generalizes the result of [7].