1
$\begingroup$

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 $f(x)=|x|^{2-n}$?

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

Polar coordinates. $\int_{\mathbb R^n} |x|^{k} dx= \int_{S^{n-1}} \int_{0}^{\infty} r^{n-1}\cdot r^{k} \enspace dr d\theta$.

| cite | improve this answer | |
$\endgroup$
  • $\begingroup$ The left-hand side equals $\infty$, right? $\endgroup$ – saz Nov 5 '14 at 19:18
  • $\begingroup$ @saz yes indeed $\endgroup$ – Haha Nov 7 '14 at 7:41

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.