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Journal of Lie Theory 15 (2005), No. 2, 429--446
Copyright Heldermann Verlag 2005

The Weak Paley-Wiener Property for Group Extensions

Hartmut Führ
Institute of Biomathematics and Biometry, GSF Research Center for Environment and Health, 85764 Neuherberg, Germany

The paper studies weak Paley-Wiener properties for group extensions by use of Mackey's theory. The main theorem establishes sufficient conditions on the dual action to ensure that the group has the weak Paley-Wiener property. The theorem applies to yield the weak Paley-Wiener property for large classes of simply connected, connected solvable Lie groups (including exponential Lie groups), but also criteria for non-unimodular groups or motion groups.

Keywords: Weak Paley-Wiener property, operator-valued Fourier transform, Mackey's theory.

MSC: 43A30, 22E27

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