Let $n$ be a non-zero natural number. Let $f$ be in $\mathcal{S}_n$. Using the result of question 13, deduce that $$\forall \theta \in \mathbb{R}, \quad |f'(\theta)| \leqslant n \|f\|_{L^\infty(\mathbb{R})}$$
Let $n$ be a non-zero natural number. Let $f$ be in $\mathcal{S}_n$. Using the result of question 13, deduce that
$$\forall \theta \in \mathbb{R}, \quad |f'(\theta)| \leqslant n \|f\|_{L^\infty(\mathbb{R})}$$