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Revista Matemática Complutense

, Volume 29, Issue 1, pp 13–57 | Cite as

The \(C^{*}\)-algebras of connected real two-step nilpotent Lie groups

  • Janne-Kathrin GüntherEmail author
  • Jean Ludwig
Article

Abstract

Using the operator valued Fourier transform, the \(C^{*}\)-algebras of connected real two-step nilpotent Lie groups are characterized as algebras of operator fields defined over their spectra. In particular, it is shown by explicit computations, that the Fourier transform of such \(C^{*}\)-algebras fulfills the norm controlled dual limit property.

Keywords

\(C^{*}\)-algebra Two-step nilpotent Lie group Fourier transform Norm controlled dual limit property 

Mathematics Subject Classification

43 (Abstract Harmonic Analysis) 

Notes

Acknowledgments

This work is supported by the Fonds National de la Recherche, Luxembourg (Project Code 3964572).

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Copyright information

© Universidad Complutense de Madrid 2015

Authors and Affiliations

  1. 1.Mathematical Research UnitUniversité du LuxembourgLuxembourgLuxembourg
  2. 2.UMR 7502, Institut Elie Cartan de LorraineUniversité de LorraineMetz Cedex 01France

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