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wu :: forums    general    complex analysis (Moderators: Icarus, william wu, SMQ, towr, Eigenray, ThudnBlunder, Grimbal)    Maximum modulus principle « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: Maximum modulus principle  (Read 4310 times) kimtahe6 Newbie     Posts: 1 Maximum modulus principle   « on: Jun 20th, 2013, 8:06am » Quote 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   . Thanks. IP Logged Pages: 1  Reply Notify of replies Send Topic Print Forum Jump: ----------------------------- riddles -----------------------------  - easy   - medium   - hard   - what am i   - what happened   - microsoft   - cs   - putnam exam (pure math)   - suggestions, help, and FAQ   - general problem-solving / chatting / whatever ----------------------------- general -----------------------------  - guestbook   - truth => complex analysis   - wanted   - psychology   - chinese « Previous topic | Next topic »

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