Good morning,
I have to find this function : $\gamma (x) = 1, \left | x \right | \leqslant 1 , x \in \mathbb{R}^n$, $\gamma \in C^\infty (\mathbb{R}^n)$ On some subset of $\mathbb{R}^n$ we can find that also : $\gamma (x) = 0$ However, I was told to use bump functions but every example I found was in $\mathbb{R}$.
The problem is that it is the first question of my exercise, and the next question, is "Show that you can find $\varpi \in L^{1}(\mathbb{R}^n)$ and $\widehat{\varpi} = \gamma$" I supposed I could take $\varpi$ = $\widehat{\gamma}$, but I am not sure...
If you could help me, it would be nice