关于高等数学中Fourier级数收敛定理的几点注记

On Convergence Theorem of Fourier Series in Advanced Mathematics

Fourier级数收敛定理是高等数学中的重要内容之一,对偏微分方程与复变函数理论的研究有着重要的作用.然而,Fourier级数收敛定理在不同的教材中表述不尽相同.通过例题说明高等数学中Fourier级数收敛定理的条件是Fourier级数收敛的充分而非必要条件,同时,指出初学者对定理的理解可能出现的误解及其原因.

Convergence theorem of Fourier series,which is an important content in advanced mathematics,plays an vital role in the theory of partial differential equation and complex variable functions.However,the convergence theorem of Fourier series expression is not the same in different materials.This paper is devoted to show that the conditions of convergence theorem of Fourier series is sufficient but not necessary by examples,and to point out some misunderstandings and its causes on convergence theorem of Fourier series for the beginners.