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        general >> complex analysis >> Prove Hardy's Theorem
        
(Message started by: immanuel78 on Dec 5^th, 2007, 10:07pm)

Title: Prove Hardy's Theorem
Post by immanuel78 on Dec 5^th, 2007, 10:07pm

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.