Let $f : R → R$ be a differentiable function and $f(x) = 0$ for $|x| ≥ 10$. Let $g(x) = \sum_{k∈Z} f(x + k)$.
Let $\displaystyle f$ be differentiable, $\displaystyle f(x)=0$ for $|x| \geq 10 $ and $g(x)=\sum_{k \in \mathbb Z}f(x+k).$