1 2 3 P 111 L LLL K Denna beh ver Nog fixas till Lite Show

Last updated: 5/20/2023

1 2 3 P 111 L LLL K Denna beh ver Nog fixas till Lite Show that if u is a harmonic function on C that is bounded above then u is constant Hint Express u as the real part of an analytic function and expo nentiate Solution Let u be the real part of the analytic function f u iv where we know that u C for some constant C Then set g eutiv where g is an entire function Now we have that g eu iv e ewv e ew eu We can se that becauce u is bounded above so is g bounded above Now we now that g is both analytic and bounded by Liouville s theorem g is constant Thus f is constant