Talk:Peter–Weyl theorem
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Initial post
editIt 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. 192.38.109.188 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)
An Example: SU(2)
editI wish there would be some references about this example. I wanted to read any further in the given references down the page but didn't find anything. Especially the justification of why the matrix coefficents are given by spherical harmonics. Can you work that up, please? — Preceding unsigned comment added by 158.181.77.247 (talk) 21:08, 16 August 2018 (UTC)