再生核空间中算子方程的解

Solution of Operator Equation in Reproducing Kernel Space

再生核空间中核的再生性在理论分析和数值逼近方面都起着非常重要的作用。本文主要利用再生核空间中有界线性算子的最佳逼近给出了算子方程的解,并对解的收敛性进行了讨论。最后,将该方法应用于积分方程,验证了该方法的有效性和可实行性。

The reproduce of kernel in reproducing kernel spaces plays an improtant role in the theoretical analysis and numerical approximation.In this paper,the solution of operator equaiton in different reproducing kernel spaces is obtained by using the best approaching operator of bounded linear operator.The convergence of the operator equation is discussed.In the final of the paper,the solution applied to integral equation demonstrates the effectiveness and achievability.