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bd3___2.2. title: Investigating whether the Fourier series of a periodic function converges or not can be a complex task. Therefore, in Engineering, they often only check the existence of the series and assume that a Fourier series converges to the original function of a periodic function.

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Investigating whether the Fourier series of a periodic function(from1) converges to the original function or not can be a complex task(참고1). Therefore, in Engineering, they often only check the existence of the series(참고2,from2) and assume that a Fourier series converges to the original function of a periodic function(참고3), except at jump discontinuities.

Can we investigate whether Fourier series converges uniformly to f or pointwise converges to f, even in cases where f is not continuous?

parse me : 언젠가 이 글에 쓰이면 좋을 것 같은 재료들.

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from : 과거의 어떤 생각이 이 생각을 만들었는가?

supplementary : 어떤 새로운 생각이 이 문서에 작성된 생각을 뒷받침하는가?

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opposite : 어떤 새로운 생각이 이 문서에 작성된 생각과 대조되는가?

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to : 이 문서에 작성된 생각이 어떤 생각으로 발전되고 이어지는가?

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참고 : 레퍼런스

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.

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.

In engineering applications, the Fourier series is generally assumed to converge except at jump discontinuities since the functions encountered in engineering are better-behaved than functions encountered in other disciplines.