Fourier级数两个收敛定理的关系及反例

The Relation Between Convergence Theorems of Fourier Series and Counterexamples

Fourier级数的收敛问题一直是很多数学研究者关注的问题,不同的数学分析教材和高等数学教材对收敛定理的表述各不相同。本文通过实例说明这些收敛定理之间不存在包含关系,并进一步说明这些收敛定理都是判别Fourier级数收敛的充分条件,而不是充要条件。

Many mathematicians have been paying attention to the problem of Fourier series＇ convergence,there are different convergence theorems in different teaching materials of Mathematical Analysis and Advanced Mathematics,this paper shows that there doesn＇t exist any inclusion relations between them and that these convergence theorems are sufficient condition,not necessary condition.