Journal of Lie Theory
Vol. 15, No. 2, pp. 429–446 (2005)
The Weak Paley-Wiener Property for Group Extensions
Hartmut FührHartmut Führ
Institute of Biomathematics and Biometry
GSF Research Center for Environment and Health
Abstract: 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
Classification (MSC2000): 43A30, 22E27
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Electronic fulltext finalized on: 20 May 2010. This page was last modified: 4 Jun 2010.