wu :: forums
wu :: forums - Maximum modulus principle

Welcome, Guest. Please Login or Register.
Jan 27th, 2022, 4:01pm

RIDDLES SITE WRITE MATH! Home Home Help Help Search Search Members Members Login Login Register Register
   wu :: forums
   general
   complex analysis
(Moderators: Icarus, Grimbal, william wu, towr, Eigenray, SMQ, ThudnBlunder)
   Maximum modulus principle
« Previous topic | Next topic »
Pages: 1  Reply Reply Notify of replies Notify of replies Send Topic Send Topic Print Print
   Author  Topic: Maximum modulus principle  (Read 4069 times)
kimtahe6
Newbie
*





   


Posts: 1
Maximum modulus principle  
« on: Jun 20th, 2013, 8:06am »
Quote Quote Modify Modify

Suppose $D=\Delta^n(a,r)=\Delta(a_1,r_1)\times \ldots  \times \Delta(a_n,r_n) \subset \mathbb{C}^n$
 
and  
 
$\Gamma =\partial \circ \Delta^n(a,r)=\left \{ z=(z_1, \ldots , z_n)\in \mathbb{C}^n:|z_j-a_j|=r_j,~ j=\overline{1,n}  \right \}$.
 
Let $f \in \mathcal{H}(D) \cap \mathcal{C}(\overline{D})$.  
 
Prove that: $\sup_{z \in \overline{D}} |f(z)|=\sup_{z \in \Gamma} |f(z)|$
 
I think we apply maximum modulus principle, but i have trouble...
Any help (or hint or another solution) would be greatly appreciated  Kiss . Thanks.
IP Logged
Pages: 1  Reply Reply Notify of replies Notify of replies Send Topic Send Topic Print Print

« Previous topic | Next topic »

Powered by YaBB 1 Gold - SP 1.4!
Forum software copyright 2000-2004 Yet another Bulletin Board