\(\displaystyle F(k) = \frac{1}{(1+k^2)^2} \)

Looking at it by inspection it seems pretty obvious to me that the approach they want me to follow is to consider

\(\displaystyle h(x) = \exp(-|x|) \)

This has a fourier transform

\(\displaystyle \tilde{h}(k) = \frac{2}{1+k^2} \)

and hence the inverse fourier transform will be a quater of the convolution of h with itself.

The problem I'm having however is with evaluating this

\(\displaystyle \int_{-\infty}^{\infty} h(y) h(x-y) dy \)

any hints?

Cheers

Simon