L^2(R)中界于S-平均连续模的光滑函数类的平均σ-K宽度

Average σ-K Width of Class of Smooth Functions With S-average Modulus of Continuity in L_2(R)

本文研究了L^2(R)中界于S-平均连续模的光滑函数类在L^2(R)尺度下的平均σ-K宽度,并且得到了d_σ(K(α,p,c),L^2(R))的精确值.同时指出B_(πσ)~2,(R)是实现d_σ(K(α,P,c),L^2(R))的平均σ维极子空间.

In this paper,the average σ-K width of some smooth functions with S-average modulus of continuity in L_2(R) is studied,and the exact value d_σ(K(α,p,c),L^2(R)) is obtained.Meanwhile,B_(πσ)~2(R) as an optimal subspace realizing d_σ(Kaα,p,c),L^2(R)) is identified.