L^2(R)中界于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 BOUNDED MODULUS OF CONTINUITY IN L^2(R)

研究了L^2(R)中一类界于连续模的光滑函数类在L^2(R)尺度下的平均σ-K宽度且得到其精确值。同时,指出B_σ(?)~2是一个极子空间。

The average σ-K width of some class of smooth functions with bounded m-th modulus of continuity in L^2(R) is studied, and its exact value is obtained. Meanwhile, B_(πσ)~2 as an optimal subspace is identified.