Solution
= Solution
The <convolution> $(g*g)(x)$ is the length of the overlap of $(-1,1)$ with $(x-1,x+1)$. This overlap has length $2-|x|$ when $|x|<2$ and zero otherwise, so $u=g*g$. The <convolution theorem> now gives
$$
\boxed{\widetilde u(k)=\widetilde g(k)^2=\frac{4\sin^2 k}{k^2},\qquad \widetilde u(0)=4.}
$$
The value at zero is also the area of the <triangular function>, providing a normalization check on its <Fourier transform>.