用Hermite函数的积分逼近积分型函数

Approximation of Integral Function by Integral of Hermite Functions

讨论了用Hermite函数的积分去逼近积分型函数的问题,给出了投影PNw(x)的原函数是平方可积的充分必要条件,得到了误差的L2(R)范数的上界.

We investigate the problem of approximating the integral function by the integral of Hermite functions. We give an equivalent condition for the primitive function of the projection P N w(x) to be square integrable. Moreover, we obtain an upper bound for the approximation error under the L 2(R) norm.