样条子空间逼近周期可微函数的最佳逼近度

THE BEST APPROXIMATION OF PERIODIC DIFFERENTIABLE CLASS APPROXIMATED BY SPLINE SUBSPACE

样条函数类与周期函数类的逼近问题是函数逼近论的重要内容。为了在较大范围内研究最佳逼近问题,在Lp空间内研究最佳逼近方法的基础上,利用最佳逼近的对偶原理、Holder不等式等工具,借助抽象逼近的方法和技巧,研究了样条子空间在Orlicz空间内的最佳逼近问题,给出了最佳逼近度的估计式。研究结果对误差估计、精度分析可提供必要的理论分析依据和参考数据。

The approximation problem of spline function and periodic function is the important content in the function approximation theory. In order to study the best approximation problem in the larger context, we adopt the method of the best approximation in Le space and the best approximation of the duality principle, Holder inequality and other tools. Based on the abstract approximation methods and techniques, we also study the optimal approximation problem of spline subspace in Orlicz space and give the best approximation degree estimation. The results of error estimation and accuracy analysis can provide necessary basis for the theoretical analysis and reference data.