Use maximum modulus principle with .
I have a function f holomorphic on D(0;R).
s, r such that (r < s < R)
M(r) = sup { |f(z)| : z = r } (r < R)
M(s) = sup { |f(z)| : z = s } (s < R)
I was asked to show that M(r) <= M(s) and I have used the Maximum Modulus and the Identity theorems to accomplish that.
The next part of question asks to show that M(r) r^(-n) >= M(s) s^(-n) when f is a polynomial of degree n 0 < r < s < R.
I know that f(z) = Sum ( Cn (z - a)^n ) from 0 to inf
and
M(r) r^(-n) >= | An |
M(s) r^(-n) >= | Bn |
Could someone push me in the right direction?
Thanks!