
Journal of Lie Theory 25 (2015), No. 4, 11251137 Copyright Heldermann Verlag 2015 A Beurling Theorem for Exponential Solvable Lie Groups Ahmad M. A. Alghamdi Dept. of Mathematical Science, Faculty of Applied Science, Umm Alqura University, P. O. Box 14035, Makkah 21955, Saudi Arabia amghamdi@uqu.edu.sa Ali Baklouti Dept. of Mathematics, Faculty of Sciences, Sfax University, Route de Soukra, 3000 Sfax, Tunisia Ali.Baklouti@fss.rnu.tn We prove in this paper an L^{2}version of Beurling's theorem for an arbitrary exponential solvable Lie group G with a nontrivial center, which encompasses the setting of nilpotent connected and simply connected Lie groups. When G has a trivial center, the uncertainty principle may fail to hold and an example is produced. The representation theory and a localized Plancherel formula are fundamental tools in the proof. Keywords: Uncertainty principle, Fourier transform, Plancherel formula. MSC: 22E25; 43A25 [ Fulltextpdf (311 KB)] for subscribers only. 