各向异性Besov类在混合范数下基于标准信息的最优恢复

Optimal recovery on anisotropic Besov classes with mixed norms by standard information

研究了各向异性Besov类中的周期函数基于标准信息的最优恢复问题.利用Vallee-Poisson算子得到逼近的上界,通过构造bump函数得到逼近的下界,进而得到渐近逼近阶.

This paper studies problems of optimal recovery on periodic functions of anisotropic Besov classes based on standard information.With the de la Vallee-Poisson operator for the proof of upper bounds and the construction of bump functions for the proof of lower bounds,the exact orders of asymptotic decay rates are obtained.