grandes-ecoles 2018 Q35

grandes-ecoles · France · centrale-maths2__mp Taylor series Prove smoothness or power series expandability of a function
Show an analogous result to Q34 for harmonic functions: for a harmonic function $g$ on $D(0,R)$, show that $\forall r \in [0, R[$, $|g(0)| \leqslant \sup_{t \in \mathbb{R}} |g(r\cos(t), r\sin(t))|$.
Show an analogous result to Q34 for harmonic functions: for a harmonic function $g$ on $D(0,R)$, show that $\forall r \in [0, R[$, $|g(0)| \leqslant \sup_{t \in \mathbb{R}} |g(r\cos(t), r\sin(t))|$.