Talk:Peter–Weyl theorem

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Mathematics rating:
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 Field:  Analysis

Initial post[edit]

It seems to me that the theorem is not stated very clearly. I other words: What exactly does the Peter-Weyl theorem say? Thanks in advance. 00:41, 5 March 2007 (UTC)

I'm not feeling confident enough about the theorem yet to write such an exposition, but I agree with this comment. Tcnuk (talk) 15:12, 8 November 2010 (UTC)
The theorem is about the regular representation of G on L2(G). The first part gives density of the matrix coefficients. The second part is a general statement about complete reducibility of unitary representations. The third part gives an explicit decomposition of the regular representation in terms of matrix elements. It might be helpful to give a quick summary of this in the lead. Unfortunately, a precise statement at that stage is probably out of the question, since even the notion of "matrix element" requires elaboration. Sławomir Biały (talk) 16:49, 8 December 2010 (UTC)

In (Bump 2004, p.24, it says that "From the point of view of harmonic analysis, these two statements are[...] equivalent", where the "statements" refer to part 1 and part 2. Then in Thm 4.3 p.25, he prooves that part 1 implies part 2 but not the other way round. Noix07 (talk) 20:09, 25 May 2014 (UTC)