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Mixing with staircase multiplicity functions

Published online by Cambridge University Press:  10 July 2008

OLEG AGEEV
OLEG AGEEV*
Affiliation:
Department of Mathematics, Moscow State Technical University, 2nd Baumanscaya St. 5, 105005 Moscow, Russia School of Mathematics and Statistics, University of New South Wales, Sydney 2052, Australia (email: [email protected], [email protected])
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Abstract

Every subgroup of the symmetric group defines a natural factor of the Cartesian power of a transformation. We calculate the set of values of the spectral multiplicity function of such factors (under certain conditions on the transformation) in terms of the number of orbits of diagonal actions of these subgroups. An analogous statement also holds on the unitary level for operators that preserve 1. In particular, we prove that for every positive integer n, there exists a transformation which is mixing of all orders and has a staircase multiplicity function of length n; that is, the essential values of the spectral multiplicity function are {1,2,…,n}.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 28 , Issue 6 , December 2008 , pp. 1687 - 1700
Copyright
Copyright © 2008 Cambridge University Press

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