No CrossRef data available.
Article contents
Bohr density of simple linear group orbits
Published online by Cambridge University Press: 09 October 2013
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
- Copyright
- © Cambridge University Press, 2013
References
Blum, J. and Eisenberg, B.. Generalized summing sequences and the mean ergodic theorem. Proc. Amer. Math. Soc. 42 (1974), 423–429.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
Kostant, B.. On convexity, the Weyl group and the Iwasawa decomposition. Ann. Sci. Éc. Norm. Sup. (4) 6 (1973), 413–455.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