# Fourier transform of power function

Assume that $$\hat f(x)= (2\pi)^{-n/2} \int_{\mathbb{R}^n} f(y) e^{-i\left<x,y\right>} dy$$ is the Fourier transform of a function $f$. What is $\hat f$ if $f(x)=|x|^{2-n}$?

• $f(x)=|x|^{2-n}$ is not even integrable. – saz Nov 5 '14 at 19:16

Polar coordinates. $\int_{\mathbb R^n} |x|^{k} dx= \int_{S^{n-1}} \int_{0}^{\infty} r^{n-1}\cdot r^{k} \enspace dr d\theta$.
• The left-hand side equals $\infty$, right? – saz Nov 5 '14 at 19:18