caa a22 4500 475740831 CHVBK 20180406123459.0 cr unu---uuuuu 170329e20001101xx s 000 0 eng 10.1023/A:1026698921311 doi (NATIONALLICENCE)springer-10.1023/A:1026698921311 Ageev O. N. É. Bauman Moscow State Technical University, Russia aut On the Spectrum of Cartesian Powers of Classical Automorphisms [Elektronische Daten] [O. Ageev] We prove the following statement: the set of all essential spectral multiplicities of $$T^{\left( n \right)} = T \times \cdot \cdot \cdot \times T$$ (n times) is $$\left\{ {n,\left( {n - 1} \right),...,n!} \right\}$$ on $$\left\{ {{\text{const}}} \right\}^ \bot$$ for Chacon transformations T, or, equivalently, the operator T(n) has a simple spectrum on the subspace C Sim of all functions that are invariant with respect to permutations of the coordinates. As an immediate consequence of this fact, we have the disjointness of all convolution powers of the spectral measure for Chacon transformations. If n=2, then T× T has a homogeneous spectrum of multiplicity 2 on $$\left\{ {{\text{const}}} \right\}^ \bot$$ , i.e., this is a solution of Rokhlin's problem for Chacon transformations. Similar statements are considered for other classical automorphisms. Plenum Publishing Corporation, 2000 unitary operator nationallicence homogeneous spectrum of multiplicity 2 nationallicence Chacon transformation nationallicence Cartesian powers nationallicence Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 68/5-6(2000-11-01), 547-551 0001-4346 68:5-6<547 2000 68 11006 https://doi.org/10.1023/A:1026698921311 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1026698921311 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Ageev O. N. É. Bauman Moscow State Technical University, Russia aut NATIONALLICENCE 773 0- Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 68/5-6(2000-11-01), 547-551 0001-4346 68:5-6<547 2000 68 11006 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer