A reproducing kernel space H~m[a,b]and its properties
Jia Yunta · Journal of Zhejiang University(Science Edition) · 2014
For the reproducing kernel space Hm[a,b]with different smoothness,this paper gives the general formula of its reproducing kernel function Rm(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 spaces closed subspace H30[a,b]is redefined,and the general formula of its reproducing kernel function R30(x,y)is provided.That is,ageneral algorithm is given to find the subspace of reproducing kernel space.