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Unformatted text preview: C , suppose that for all holomorphic functions F : D (0 , 1) U the function f F is subharmonic. Prove that f itself is subharmonic. (4) Let f C 2 ( U ) for some open U C . Suppose f is subharmonic. Show that f 0 on U . (Hint: Taylor expansion) Now suppose f > 0 on U , show that f is subharmonic. (Hint: f has no local maxima) Finally suppose f 0 on U , show that f is subharmonic. (Hint: Consider ( f + | z | 2 )). 1...
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This document was uploaded on 12/08/2010.
- Spring '09