L_(2)上复变函数的傅里叶级数逼近  

The Fourier series approximation of complex functions in L_(2)

作　　者：杨刚 谷懿 YANG Gang;GU Yi(School of Mathematics and Statistic,Yunnan University,Kunming 650500,Yunnan,China)

机构地区：[1]云南大学数学与统计学院,云南昆明650500

出　　处：《云南大学学报（自然科学版）》2021年第6期1059-1070,共12页Journal of Yunnan University(Natural Sciences Edition)

基　　金：国家自然科学基金(11761077)。

摘　　要：考虑定义在圆盘U={z∈C:1/2<|z|<1}上解析且原点为其本性奇点的特殊复函数类的逼近.得2到最佳逼近E_(n-1)(f)_(2)分别与函数z^(r)f^((r))的m阶连续模及K泛函的精确Jackson不等式.然后,研究最佳逼近E_(n-1)(f)_(2)与函数z^(r)f^((r))的m阶连续模在区间(0,h)上的加权积分之间关系,得到相应的精确Jackson不等式.最后,得到关于函数z^(r)f^((r))的m阶连续模,函数z^(r)f^((r))的m阶连续模在区间(0,h)上的加权积分和K泛函等函数类上的最佳逼近及n维宽度.We consider the approximation of a special class of complex functions f that is analytic on the disk U={z∈C:1/2<|z|<1},whose origin is its essential singularity.We obtain the exact Jackson inequality between the best approximation E_(n-1)(f)_(2)of functions f and m-order continuous modules of functions z^(r)f^((r)).We also obtain the exact Jackson inequality between the best approximation E_(n-1)(f)_(2)of function f and K-functional.Then we obtain the exact Jackson inequality between the best approximation E_(n-1)(f)_(2)of functions f and weighted integral of m-order continuous modules of functions z^(r)f^((r)).Finally,we obtain the best approximation and n-widths in the functions classes of m-order continuous modules of functions z^(r)f^((r)),in the functions classes of weighted integral of m-order continuous modules of functions z^(r)f^((r))and in the functions classes of K-functional respectively.

关 键 词：最佳逼近 m阶连续模 K泛函 n维宽度 

分 类 号：O174.41[理学—数学]