I’m struggling with the following problem: What is a function such that it is not equal to the inverse Fourier transform of its Fourier transform?
2026-04-19 00:57:47.1776560267
Inverse Fourier transform of a Fourier transform
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A fourier transform does not imply uniqueness. It is defined by an integral, and an integral is "blind" to single points. For example consider the function $f(x)=x^2$ and $g(x)=f(x)$ almost everywhere (suppose when $x=0, g(x)=20)$.
Both functions have the same fourier transform (as it is defined by an integral), thus will have the same inverse transform, and such as it is both $g(x), f(x)$ will be equal after the transform+inverse transform to $f(x)$.