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Fourier inversion formula for discrete nilpotent groups

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  09 April 2009

Tsuyoshi Kajiwara
Tsuyoshi Kajiwara
Affiliation:
Department of Mathematics, College of Liberal Arts and Sciences, Okayama UniversityTsushima, Okayama, Japan
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Abstract

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Let G be a countable torsion free finitely generated nilpotent group. Then the Fourier transform can be considered as a map from the space of bounded degree 1 random operators to the Fourier algebra A(G). In this paper, we recover the matrix elements of a positive random variable from the corresponding positive definite function in A(G) for such a group.

MSC classification

Secondary: 46L55: Noncommutative dynamical systems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 46 , Issue 3 , June 1989 , pp. 415 - 422
Copyright
Copyright © Australian Mathematical Society 1989

References

[1]Connes, A., ‘Sur la theorie non commutative de l'integration’ (pp. 19–143, Lecture Notes in Math., vol. 725, Springer-Verlag).Google Scholar
[2]Paterson, A. L. T., ‘A transform for Fourier algebras of the Heisenberg group’, preprint.Google Scholar
[3]Pedersen, G. K. and Takesaki, M., ‘The Radon Nikodym theorem for von Neumann algebras’, Acta Math. 130 (1973), 53–88.Google Scholar
[4]Sutherland, C. E., ‘Cartan subalgebras, transverse measures and non-type I Plancherel formulae’, J. Funct. Anal. 60 (1985), 281–308.CrossRefGoogle Scholar