对“微波共振跃迁法测量电子偶素2~3S_1-2~3P_1精细结构”实验拟合公式的探讨

本文对Michigan大学S.Hatamian等人在“微波共振跃迁法测量电子偶素2~3S_1-2~3P_J精细结构”实验中所用拟合公式进行了审慎的分析和推证,修正了该公式的功率增宽项,并就Mainz大学R.Ley等人对该公式的批评作了评价。最后,采用新、旧拟合公式对Michigan组实验数据进行拟合并讨论其结果。     

Constructive methods of approximation by ridge functions and radial functions

Let be a univariant function, and letg(x) be the average of (x,u) asu runs over the unit sphere in ⁿ . We give a necessary and sufficient condition forg to be a kernel function, i.e., thatg be inL ¹ ( ⁿ ) and have integral 1. The result is used to give a constructive proof of the density of the ridge functions based upon the function .