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On a question of R. Godement about the spectrum of positive, positive definite functions

Published online by Cambridge University Press:  24 October 2008

Mohammed B. Bekka
Mohammed B. Bekka
Affiliation:
Mathematisches Institut, Technische Universität München, Arcisstraβe 21, W-8000 München 2, Germany
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Extract

Let G be a locally compact group, and let P(G) be the convex set of all continuous, positive definite functions ø on G normalized by ø(e) = 1, where e denotes the group unit of G. For ø∈P(G) the spectrum spø of ø is defined as the set of all indecomposable ψ∈P(G) which are limits, for the topology of uniform convergence on compact subsets of G, of functions of the form

(see [5], p. 43). Denoting by πø the cyclic unitary representation of G associated with ø, it is clear that sp ø consists of all ψ∈P(G) for which πψ is irreducible and weakly contained in πø (see [3], chapter 18).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 110 , Issue 1 , July 1991 , pp. 137 - 142
Copyright
Copyright © Cambridge Philosophical Society 1991

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References

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