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wu :: forums    general    complex analysis (Moderators: Eigenray, ThudnBlunder, towr, SMQ, william wu, Icarus, Grimbal)    Prove Hardy's Theorem « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: Prove Hardy's Theorem  (Read 6843 times) immanuel78 Newbie     Gender: Posts: 23 Prove Hardy's Theorem   « on: Dec 5th, 2007, 10:07pm » Quote Modify If f is anaytic on B(0;R) and not constant then   I(r)=( 1/(2*pi) ) int[ from 0 to 2*pi ] |f( r*exp(i*t) )| dt   is strictly increasing and log I(r) is a convex function of log r.     « Last Edit: Dec 6th, 2007, 2:59am by immanuel78 » 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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