The Convergence of Fourier Series at Jump Discontinuity
Автор: DrAvitech
Загружено: 2025-08-13
Просмотров: 135
There are many known sufficient conditions for the Fourier series of a function to converge at a given point x, for example if the function is differentiable at x.
Even a jump discontinuity does not pose a problem: if the function has left and right derivatives at x, then the Fourier series converges to the average of the left and right limits.
The Fourier Series converges to f (x) at all points at which f is continuous and to the average value at all points at which f is discontinuous.
Thus a Fourier Series converges to the average value of the left and right limits at a point of discontinuity.
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#fourierseries
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#discontinuity
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