RE: L2 inner product. Integrate and Conjugate?

*To*: mathgroup at smc.vnet.net*Subject*: [mg36339] RE: [mg36308] L2 inner product. Integrate and Conjugate?*From*: "David Park" <djmp at earthlink.net>*Date*: Mon, 2 Sep 2002 04:08:48 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Andreas, inner[f_Function, g_Function] := Integrate[ComplexExpand[Conjugate[f[x]]]*g[x], {x, -1/2, 1/2}] inner[# &, # &] 1/12 I'm not too knowledgable about using complex functions in Mathematica but sometimes I think that "ComplexExpand" should be renamed "ComplexSimplify". One very often needs it. David Park djmp at earthlink.net http://home.earthlink.net/~djmp/ From: Andreas Dietrich [mailto:andreas.dietrich at physik.uni-marburg.de] To: mathgroup at smc.vnet.net 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.