# What's the Fourier transform of these functions?

1. The Fourier transform of $|x|^{\alpha}$.

This is the Fourier transform of a homogeneous function, and there are several cases of various $\alpha$: when $a\leq -n$, it's not a temperate distribution; when $-n<\alpha<0$,then the Fourier transform is $c_{n}|\xi|^{-n+\alpha}$, where $c_{n}$ is some constant; when $\alpha=2k$,a positive even number, then it's Fourier transformation is $(-\Delta)^{k}\delta_{0}$.

My question is when $\alpha$ is any positive number (not the even case), then what's the Fourier transform of it ?

2. The Fourier transform of $e^{it|x|}$ ?

(the Fourier transforms I have mentioned here are in the sense of temperate distributions)

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 What is $n$? (need more characters) – Fabian Aug 16 '12 at 11:51 n is the dimension of the space – sun Aug 16 '12 at 13:17