APM346-2022S > Chapter 5

Theorem 3 in chapter 5 question

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Weihan Luo:
In property 3 of Theorem 3 ($g(x) =𝑥𝑓(𝑥)⟹𝑔̂(𝑘)=i\hat{f}'(k)$), for $\hat{f}'(k)$, is the Fourier transform being computed before the derivative, or the other way around? Intuitively, Leibnitz rule says that the order shouldn't matter here, but I just want to get a confirmation. Thank you

Victor Ivrii:
It is the derivative of Fourier transform; otherwise it would be $\widehat{f'}(k)$ and covered by another property