摘要
具有Ｏ正则变化拟单调系数的Ｆｏｕｒｉｅｒ级数的复值函数ｆ的Ｌ１逼近的特征之一是：‖ｆ－Ｓｎ（ｆ）‖＝Ｏ（ψｎ）Ｅｎ（ｆ）＝Ｏ（ψｎ）和＾ｆ（ｎ）ｌｏｇ｜ｎ｜＝Ｏ（ψ｜ｎ｜），这里Ｓｎ（ｆ）是部分和算子，｛ψｎ｝是一个单调递减趋于零的数列，满足ψｎ＝Ｏ（ψ２ｎ）．现问在什么情况下条件Ｅｎ（ｆ）＝Ｏ（ψｎ）可以省去？本文讨论这个问题，并给出一些肯定的回答．
Xie and Zhou establishes some nice results for L 1 Approximation of Fourier series of complex valued functions with O regularly varying quasimonotone coefficients. Exactly, one result says that ‖f-S n(f)‖=O(ψ n)E n(f) L=O(ψ n) and (n) log |n| =O (ψ |n| ) , where {ψ n} is a decreasing null sequence satisfying ψ n=O(ψ 2n ) . It is natural to ask if the condition E n(f) L=O(ψ n) can be removed under some conditions? The persent paper will investigate this question.
出处
《杭州大学学报（自然科学版）》
CSCD
1998年第3期19-25,共7页
Journal of Hangzhou University Natural Science Edition
关键词
复值函数
L^1-逼近
傅里叶级数
傅里叶系数
complex valued function
Fourier series
Fourier coefficient
O regularly varying quasimonotone
L 1 approximation
