L2 inner product. Integrate and Conjugate?
- To: mathgroup at smc.vnet.net
- Subject: [mg36308] L2 inner product. Integrate and Conjugate?
- From: Andreas Dietrich <andreas.dietrich at physik.uni-marburg.de>
- Date: Sat, 31 Aug 2002 01:25:50 -0400 (EDT)
- Reply-to: andreas.dietrich at firemail.de
- Sender: owner-wri-mathgroup at wolfram.com
Hello.
I am trying to implement the inner product in the space of
complex-valued, square integrable functions over [-1/2,1/2], which can
be expressed in Mathematica code as
inner[f_Function,g_function]:=Integrate[Conjugate[f[x]]*g[x],{x,-1/2,1/2}]
This is simple enough. Problem is, Mathematica seamingly cannot
evaluate the Integral for even the simplest of functions:
In[10]:=inner[#&,#&]
Out[10]:=\!\(\[Integral]\_\(-\(1\/2\)\)\%\(1\/2\)\(x\ Conjugate[
x]\) \[DifferentialD]x\)
As you see, the Integrate returns unevaluated. It works fine if I
remove the Conjugate. Unfortunately the Conjugate is needed for
positive definiteness.
Various variants with Composition, Re and Im etc. don't work either.
This should be a So how do I get Integrate to work with Conjugate?
I use Mathematica 4.1.2.0 on Linux/i386.
Thank you,
Andreas
--
True Pleasure in this society is more dangerous than bank robbery.