It is shown that if are algebraic elements in generating a dense subgroup, then the corresponding Hecke operator has a spectral gap.
On démontre que si sont des éléments algébriques de et le groupe engendré par est dense, alors l'opérateur de Hecke défini par ces éléments a un trou spectral.
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Jean Bourgain 1; Alexander Gamburd 2
@article{CRMATH_2010__348_11-12_609_0, author = {Jean Bourgain and Alexander Gamburd}, title = {Spectral gaps in $ \mathit{SU}(d)$}, journal = {Comptes Rendus. Math\'ematique}, pages = {609--611}, publisher = {Elsevier}, volume = {348}, number = {11-12}, year = {2010}, doi = {10.1016/j.crma.2010.04.024}, language = {en}, }
Jean Bourgain; Alexander Gamburd. Spectral gaps in $ \mathit{SU}(d)$. Comptes Rendus. Mathématique, Volume 348 (2010) no. 11-12, pp. 609-611. doi : 10.1016/j.crma.2010.04.024. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.04.024/
[1] Products of Random Matrices with Applications to Schrödinger Operators, Birkhäuser, 1985
[2] On the Erdos–Volkmann and Katz–Tao ring conjectures, Geom. Funct. Anal., Volume 13 (2003) no. 2, pp. 334-365
[3] J. Bourgain, The discretized ring and projection theorems, J. Anal., in press
[4] On the spectral gap for finitely generated subgroups of , Invent. Math., Volume 171 (2008) no. 1, pp. 83-121
[5] Expansion and random walks in , II, J. Eur. Math. Soc. (JEMS), Volume 11 (2009) no. 5, pp. 1057-1103
[6] On dense free subgroups of Lie groups, J. Algebra, Volume 261 (2003) no. 2, pp. 448-467
[7] Additive Combinatorics, Cambridge Stud. Adv. Math., vol. 105, 2006
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