Toronto Math Forum
APM3462022S => APM346Lectures & Home Assignments => Chapter 5 => Topic started by: Weihan Luo 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

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