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Bohr density of simple linear group orbits

Published online by Cambridge University Press:  09 October 2013

ROGER HOWE  and
FRANÇOIS ZIEGLER
ROGER HOWE
Affiliation:
Department of Mathematics, Yale University, New Haven, CT 06520-8283, USA email howe@math.yale.edu
FRANÇOIS ZIEGLER
Affiliation:
Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA 30460-8093, USA email fziegler@georgiasouthern.edu
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Abstract

We show that any non-zero orbit under a non-compact, simple, irreducible linear group is dense in the Bohr compactification of the ambient space.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 35 , Issue 3 , May 2015 , pp. 910 - 914
Copyright
© Cambridge University Press, 2013 

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References

Berger, M.. Geometry. I. Springer-Verlag, Berlin, 1987.Google Scholar
Blum, J. and Eisenberg, B.. Generalized summing sequences and the mean ergodic theorem. Proc. Amer. Math. Soc. 42 (1974), 423–429.Google Scholar
Bourbaki, N.. Integration. I. Springer, Berlin, 2004, Chs 1–6.Google Scholar
Dixmier, J.. C ∗-algebras. North-Holland, Amsterdam, 1982.Google Scholar
Galindo, J., Hernández, S. and Wu, T.-S.. Recent results and open questions relating Chu duality and Bohr compactifications of locally compact groups. Open Problems in Topology. II. Ed. Pearl, E.. Elsevier, Amsterdam, 2007, pp. 407–422.Google Scholar
Graham, C. C. and Carruth McGehee, O.. Essays in Commutative Harmonic Analysis. Springer, New York, 1979.Google Scholar
Hewitt, E. and Ross, K. A.. Abstract Harmonic Analysis. Vol. 1 Springer, Berlin, 1963.Google Scholar
Katznelson, Y.. Sequences of integers dense in the Bohr group. Proc. Roy. Inst. Tech. (Stockholm) (June 1973) 79–86, available at http://math.stanford.edu/~katznel/.Google Scholar
Knapp, A. W.. Lie Groups beyond an Introduction. Birkhäuser, Boston, 2002.Google Scholar
Kostant, B.. On convexity, the Weyl group and the Iwasawa decomposition. Ann. Sci. Éc. Norm. Sup. (4) 6 (1973), 413–455.Google Scholar
Petersen, K.. Ergodic Theory. Cambridge University Press, Cambridge, 1983.Google Scholar
Rogers, K. M.. Sharp van der Corput estimates and minimal divided differences. Proc. Amer. Math. Soc. 133 (2005), 3543–3550.CrossRefGoogle Scholar
Stein, E. M.. Harmonic Analysis: Real-variable Methods, Orthogonality, and Oscillatory Integrals. Princeton University Press, Princeton, NJ, 1993.Google Scholar
Ziegler, F.. Subsets of ${R}^{n} $ which become dense in any compact group. J. Algebraic Geom. 2 (1993), 385–387.Google Scholar
Ziegler, F.. Méthode des orbites et représentations quantiques. PhD Thesis, Université de Provence, Marseille, 1996, arXiv:1011.5056.Google Scholar