Definition: Let be $u$ and $v$ two sequences the convolution of these sequences is defined than $h(m)=u(m)* v(m) = \sum_{s=-\infty}^{\infty}u(m-s)v(s).$
Question: Show that $\sum_{m=-\infty}^{\infty}h(m)=\sum_{m=-\infty}^{\infty}u(m)\sum_{m=-\infty}^{\infty}v(m)$.
I want know if is posible solve this using convolution theorem for sequences (*) I trying ...
$H(w)=U(w)V(w) = \sum_{m=-\infty}^{\infty}u(m)\exp(-j m w)\sum_{m=-\infty}^{\infty}v(m)\exp(-j m w),$
but I don't what else to do.
*Theorem: The Fourier transform of $h(m)=u(m)* v(m)$ is $H(w)=U(w)V(w).$