Hi, I have the follow question:

Construct a function $\displaystyle \phi\in C_c^\infty (\mathbb{R})$ such that $\displaystyle \phi\geq 0$, $\displaystyle supp\phi\subset (-1,1)$

$\displaystyle \psi_n(x)=\phi(x-n)/\displaystyle_{m\in\mathbb{Z}}\phi(x-m),\;\;\; n\in\mathbb{Z}$

are a partition of unity subordinated to the cover $\displaystyle \cup_{n\in\mathbb{Z}}(n-1,n+)$ of $\displaystyle \mathbb{R}$.

Thanks!!