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Dynamical systems on translation bounded measures: pure point dynamical and diffraction spectra

Published online by Cambridge University Press:  25 October 2004

MICHAEL BAAKE  and
DANIEL LENZ
MICHAEL BAAKE
Affiliation:
Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany (e-mail: [email protected])
DANIEL LENZ
Affiliation:
Fakultät für Mathematik, TU Chemnitz, 09107 Chemnitz, Germany (e-mail: [email protected])
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Abstract

Certain topological dynamical systems that arise from actions of $\sigma$-compact locally compact Abelian groups on compact spaces of translation bounded measures are considered. Such a measure dynamical system is shown to have a pure point dynamical spectrum if and only if its diffraction spectrum is pure point.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 24 , Issue 6 , December 2004 , pp. 1867 - 1893
Copyright
2004 Cambridge University Press

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