ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
Let G be a locally compact group, which need not be unimodular. Let x→U(x) (x∈G) be an irreducible unitary representation of G in a Hilbert space H(U). Assume that U is square integrable, i.e., that there exists in H(U) at least one nonzero vector g such that ∫||(U(x)g,g)||2 dx〈∞. We give here a reasonably self-contained analysis of the correspondence associating to every vector f∈H(U) the function (U(x)g,f) on G, discussing its isometry, characterization of the range, inversion, and simplest interpolation properties. This correspondence underlies many properties of generalized coherent states.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.526761
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