Fourier Transformation of Absolute Values to negative Powers

62 Views Asked by At

I consider the Fourier Transformation of an Absolute Value, i.e.

$$ \int_{-\infty}^{\infty} \frac{e^{ikx}}{|x|^{a/2}}dx, $$

with $a \in \mathbb{N}_{>0}$. I'm not able to find a solution for this integral. Does anybody know what the solution is or if an solution exists?

greetz

mike