APPROXIMATION OF SPHERICAL MEANS OF MULTIPLE FOURIER INTEGRALS AND FOURIER SERIES ON SET OF FULL MEASURE

In this paper we consider the approximation for functions in some subspaces of L^2 by spherical means of their Fourier integrals and Fourier series on set of full measure. Two main theorems are obtained.

Fejer定理的一种多元推广

将一元傅立叶分析中关于傅氏级数及其共轭级数之间的收敛性关系的Ｆｅｊｅｒ定理推广到多元情形。主要结果为定理：若函数ｆ∈Ｌ（Ｅｋ）（ｋ≥２）的傅氏积分的球形平均σＲ（ｆ；ｘ）在域Ｄ内一致收敛，则它的共轭傅氏积分的球形平均σ↑￣Ｒ（ｆ；ｘ）在其（Ｃ，１）可和点处一定收敛。