Geodesic
A Beurling Theorem for Exponential Solvable Lie Groups
Journal of Lie theory, Tome 25 (2015) no. 4, pp. 1125-1137
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We prove in this paper an L2-version of Beurling's theorem for an arbitrary exponential solvable Lie group G with a non-trivial 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.
Classification : 22E25, 43A25
Mots-clés : Uncertainty principle, Fourier transform, Plancherel formula 
@article{JLT_2015_25_4_JLT_2015_25_4_a8,
     author = {A. M. A. Alghamdi and A. Baklouti},
     title = {A {Beurling} {Theorem} for {Exponential} {Solvable} {Lie} {Groups}},
     journal = {Journal of Lie theory},
     pages = {1125--1137},
     year = {2015},
     volume = {25},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JLT_2015_25_4_JLT_2015_25_4_a8/}
}
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A. M. A. Alghamdi; A. Baklouti. A Beurling Theorem for Exponential Solvable Lie Groups. Journal of Lie theory, Tome 25 (2015) no. 4, pp. 1125-1137. http://geodesic.mathdoc.fr/item/JLT_2015_25_4_JLT_2015_25_4_a8/