Suppose \(P(z)=a_nz^n+\cdots +a_0\). If \(M(\rho )=\sup _\theta |P(\rho e^{i\theta })|\) then show that \[ \frac {M(r)}{r^n}\ge \frac {M(R)}{R^n} \] if \(0<r<R\).
Question
Math 6210 • Real Analysis
Fall 1995 • Question 7
Question
Fall 1995 • Question 7
Suppose \(P(z)=a_nz^n+\cdots +a_0\). If \(M(\rho )=\sup _\theta |P(\rho e^{i\theta })|\) then show that \[ \frac {M(r)}{r^n}\ge \frac {M(R)}{R^n} \] if \(0<r<R\).