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MathGroup Archive 1999

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addendum to real valued expressions in Mathematica 4.0

  • To: mathgroup at smc.vnet.net
  • Subject: [mg18470] addendum to real valued expressions in Mathematica 4.0
  • From: "Andrzej Kozlowski" <andrzej at tuins.ac.jp>
  • Date: Wed, 7 Jul 1999 23:08:37 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

Daniel Lichtblau has reminded me that I have forgotten my complex analysis.
In my message on real valued expressions in Mathematica 4.0 I wrote:

> However, there are still some simplifications which are  pretty obvious to
> humans that Mathematica seems unable to manage. For example, It is easy to
> prove that if f is a function holomorphic in some domain containing a real
> interval and symmetric with respect to conjugation  and if f takes real
> values on the real interval within its domain then
> f[Conjugate[z]] == Conjugate[f[z]] and hence f[z]+f[Conjugate[z]] is always
> real. For example


Well, of course, one need not assume the domain to be symmetric with respect
to conjugation for this follows from the other assumptions. This is the well
known "reflection principle" (e.g. see Ahlfors, "Complex Analysis", Theorem
24.) Well, my excuse is that it has been a long time since my undergaduate
days and nowadays almost always any topological spaces that come my way have
dimension at least 3.
--
Andrzej Kozlowski
Toyama International University
JAPAN
http://sigma.tuins.ac.jp
http://eri2.tuins.ac.jp



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