1. Does there exist function $f$ such that:
1) $f\in C_0^\infty(\mathbf{R}^n)$, $f$ is supported in $\{x:|x|\leq 2\}$;
2) $f(x)\equiv 1$, if $|x|\leq 1$;
3) $f(x)\geq 0, \, \hat f(\xi)\geq 0$.
2. Does there exist function $f$ such that:
1) $f\in C_0^\infty(\mathbf{R}^n)$, $f$ is supported in $\{x:1/2\leq |x|\leq 4\}$;
2) $f(x)\sim 1$, if $1\leq |x|\leq 2$;
3) $f(x)\geq 0,\, \hat f(\xi)\geq 0$.