Re: sum of real and imaginary parts constant?
- From: israel@xxxxxxxxxxx (Robert Israel)
- Date: 18 Dec 2006 19:51:35 GMT
In article <1166428150.098160.284810@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
<bensaou@xxxxxxxxx> wrote:
Hey, my flat-mates left this problem on the fridge, and its driving me
nuts! (game we play...)
Let f be an entire function such that Re(f(z))+Im(f(z)) < 1 for all z.
Show that f is constant.
So far, I've got that f is holomorphic and entire...
Thanks for any help!
Hint: Apply a fractional linear transformation and then use
Liouville's Theorem.
Robert Israel israel@xxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
.
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