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November 2nd, 2011, 08:45 PM  #1 
Newbie Joined: Nov 2011 Posts: 8 Thanks: 0  Derivative Estimates
An entire function f obeys the estimate f(z)<= me^(alpha*x) for all points z=x+iy, where m and alpha are positive constants. Verify that f has the form f(z) = Ae^alpha*z for some constant A. Could one draw the same conclusion if one knew only that f(z)<=me^alpha*z held for every z?


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