Author Topic: Theorem 3 in chapter 5 question  (Read 685 times)

Weihan Luo

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Theorem 3 in chapter 5 question
« on: March 17, 2022, 12:16:07 AM »
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

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Re: Theorem 3 in chapter 5 question
« Reply #1 on: March 18, 2022, 08:17:41 AM »
It is the derivative of Fourier transform; otherwise it would be $\widehat{f'}(k)$ and covered by another property