再生核空间H(K)中的二阶微分算子插值样条

The Second Order Differential Operator Interpolation Spline in the Reproducing Kernel Space H(K)

讨论再生核H（K）空间中的样条函数,给出了其等价性条件;证明了它的一个二阶微分算子插值样条既可由再生核函数表示又可由折线函数表示,这不仅在理论上便于获得此种插值样条函数的最佳性质,而且在应用上也便于数值计算.

In this paper, authors discuss the spline function in the reproducing kernel space H(K), give its equivalent relations and prove that its 2-th differential operator interpolation spline function is expressed not only by the reproducing kernels but also by polygonal functions. So in the theory, it can be easy to prove its' best properties and the method is convenient for numeric calculation in applications, too.