Topological Group Case
For a topological group G, the regular representation in the above sense should be replaced by a suitable space of functions on G, with G acting by translation. See Peter-Weyl theorem for the compact case. If G is a Lie group but not compact nor abelian, this is a difficult matter of harmonic analysis. The locally compact abelian case is part of the Pontryagin duality theory.
Read more about this topic: Regular Representation
Famous quotes containing the words group and/or case:
“I can’t think of a single supposedly Black issue that hasn’t wasted the original Black target group and then spread like the measles to outlying white experience.”
—June Jordan (b. 1936)
“In the case of pirates, say, I would like to know whether that profession of theirs has any peculiar glory about it. It sometimes ends in uncommon elevation, indeed; but only at the gallows.”
—Herman Melville (1819–1891)