缓增样条的平均维数及逼近阶

MEAN DIMENSION OF TEMPERED SPLINE AND ITS APPROXIMATION ORDER

确定了r阶缓增样条类的平均维数的精确估计，并证明了缓增样条函数类是Soborev类Wr2（R）在L2（R）尺度下的一个最优子空间．

The exact estimate of mean dimension for the class of tempend splines of order r is determined, and it is also proved that the subspace of tempered splines is asymptotic optimal for average width of the sobolev dass W^r_2(R) in metric L_q, 2≤q≤.