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On the multiplicity function of generic group extensions with continuous spectrum

Published online by Cambridge University Press:  30 March 2001

OLEG N. AGEEV
OLEG N. AGEEV
Affiliation:
Department of Mathematics, Moscow State Technical University, 107005 Moscow, Russia (e-mail: ageev@mx.bmstu.ru)
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Abstract

A modification of the method of geometric models is proposed and applied to the study of multiplicity functions of group extensions.

It is proved that, for some generic set of the automorphisms T of the Lebesgue space with respect to the standard topology, for any M\subseteq {\mathbb N} \cup \{\infty\}(1\in M) there exists a generic set of weakly mixing group extensions T' of transformation T with M(T')=M, where M(T) denotes the set of essential spectral multiplicities of the unitary operator corresponding to the transformation T.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 21 , Issue 2 , April 2001 , pp. 321 - 338
Copyright
2001 Cambridge University Press

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