Past exam of the analysis course of the University of Oxford / 2011 / 4 / b / v

Evaluation at zero is a bounded linear functional for the uniform norm. DefineIt is linear and satisfies $|\varphi (f)|\le \sqrt{2\pi }\Vert T\Vert \Vert f{\Vert }_{\infty }$. Since $e_n(0)=(2\pi {)}^{-1/2}$,The factor $\sqrt{2\pi }$ is required by the source's basis normalization.