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

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2023/05/07 13:56

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1 more property

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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.

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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.