Good afternoon,
I need to show that there is a function $\gamma$ that is infinite derivative and where every element of a subset of $\mathbb{R}^n$ gives $\gamma (x) = 0$ Also, this function must respect this : $\gamma (x) = 1, \left | x \right | \leqslant 1 , x \in \mathbb{R}^n$
For now, I found that $\gamma (x) = \chi[0;1](\left | x \right |)$. I guess I need to regularize my function, however I don't really know how to process...
If you can give me a hint, it would be nice