Abstract
We study the behaviour of the maximal spectral multiplicity for the powers of a weakly mixing automorphism . For some particular infinite sets we show that there exists a weakly mixing rank-one automorphism such that and for all positive integers . Moreover, the cardinality of the set of spectral multiplicities for the power is shown to satisfy the conditions and , , . We also construct another weakly mixing automorphism with the following properties: all powers have homogeneous spectra and the set of limit points of the sequence is infinite.Bibliography: 17 titles.
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