❓

how can we check if the Fourier series converges to the original periodic function well?

상태

해결되지 않은 궁금증

생성일

2023/05/07 14:27

관련태그

1 more property

질문을 구체화할 수 있는 메모들

1.

A proof that a Fourier series is a valid representation of any periodic function (that satisfies the Dirichlet conditions) is overviewed in § Fourier theorem proving convergence of Fourier series.

2.

the question of whether the Fourier series of a periodic function converges to a given function is researched by a field known as classical harmonic analysis, a branch of pure mathematics. Convergence is not necessarily given in the general case, and certain criteria must be met for convergence to occur. Determination of convergence requires the comprehension of pointwise convergence, uniform convergence, absolute convergence, Lp spaces, summability methods and the Cesàro mean.

질문을 해소하기 위해 해소해야 하는 질문들

1.

how we can rely on Fourier's assertion that any periodic function can be represented as a sum of periodic functions such as trigonometric functions.

질문과 관련한 답을 작성한 글들

1.

None