MTH 282 Lecture Notes - Lecture 6: Ponceau 4R
7 May 2020
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Thm let f be analytic inside add on centered at zo if. Ifcz iem az on cr then a circle cr of radius r lfcmc. az en ptnm forn hz. Liouville"s 1hm the only bounded entire functions are the constant functions. Every inconstant polynomial with complex coefficients has at. Lemma suppose f is analytic in a disk centered at zo and that least one root the disk is ifczo1 the maximum value of hail over. Candy"s integral formula for f analytic in a circle cr of radius r dzpanametorisecr zqlzfnfz. azo. Z zo re2its0ete 21 fcz. in fo2ttfcffeereiiireitdt zjo2ttfczorezt at mean valueof fez alongcp. If f b analytic in a domain d and itcz1 attains its maximum value at is constant in d inside d then f a point. Ei find the maximum value of 122 32 11 on the disk 121el. I243z l l e 124 13121 11 e5.
