1Dept. of Mathematical Science, Faculty of Applied Science, Umm Alqura University, P. O. Box 14035, Makkah 21955, Saudi Arabia 2Dept. of Mathematics, Faculty of Sciences, Sfax University, Route de Soukra, 3000 Sfax, Tunisia
Journal of Lie Theory, Tome 25 (2015) no. 4, pp. 1125-1137
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.
1
Dept. of Mathematical Science, Faculty of Applied Science, Umm Alqura University, P. O. Box 14035, Makkah 21955, Saudi Arabia
2
Dept. of Mathematics, Faculty of Sciences, Sfax University, Route de Soukra, 3000 Sfax, Tunisia
Ahmad M. A. Alghamdi; Ali 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/JOLT_2015_25_4_a8/
@article{JOLT_2015_25_4_a8,
author = {Ahmad M. A. Alghamdi and Ali 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/JOLT_2015_25_4_a8/}
}
TY - JOUR
AU - Ahmad M. A. Alghamdi
AU - Ali Baklouti
TI - A Beurling Theorem for Exponential Solvable Lie Groups
JO - Journal of Lie Theory
PY - 2015
SP - 1125
EP - 1137
VL - 25
IS - 4
UR - http://geodesic.mathdoc.fr/item/JOLT_2015_25_4_a8/
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%F JOLT_2015_25_4_a8
