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)

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.