一类再生核空间H^m[a,b]及其性质

A reproducing kernel space H^m[a,b]and its properties

对于光滑度各异的再生核空间Hm[a,b]未使用经典的广义函数δ(t),而用新方法和新技巧求得了再生核Rm(x,y)的通式,给出了再生核一些新的性质,并证明了再生核Rm(x,y)是关于变量x的2 m-1阶样条函数,再生核空间Hm[a,b]与其他相应的再生核空间是等价的.最后,对带有各类边值条件的再生核闭子空间H30[a,b],给出了新的定义和再生核函数R30(x,y)的通式,亦即给出了再生核子空间再生核的通用算法.

For the reproducing kernel space H^m[a,b]with different smoothness,this paper gives the general formula of its reproducing kernel function R^m（x,y）by a new method.It is proved to be a 2 m-1order spline function of the variable x.Moreover,some new properties of this reproducing kernel function are discussed,and the theory analysis shows that the reproducing kernel space we proposed is equivalent to other ones.Finally,the reproducing kernel spaces closed subspace H0^3[a,b]is redefined,and the general formula of its reproducing kernel function R0^3（x,y）is provided.That is,ageneral algorithm is given to find the subspace of reproducing kernel space.