Geodesic
Spectral multiplicities and asymptotic operator properties of actions with invariant measure
Sbornik. Mathematics, Tome 200 (2009) no. 12, pp. 1833-1845

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New sets of spectral multiplicities of ergodic automorphisms of a probability space are proposed. Realizations have been obtained, inter alia, for the sets of multiplicities $\{p,q,pq\}$, $\{p,q,r,pq,pr,rq,pqr\}$ and so on. It is also shown that systems with homogeneous spectrum may have factors over which they form a finite extension. Moreover, these systems feature arbitrary polynomial limits, and thus may serve as useful elements in constructions. A so-called minimal calculus of multiplicities is proposed. Some infinite sets of multiplicities occurring in tensor products are calculated, which involve a Gaussian or a Poisson multiplier. Spectral multiplicities are also considered in the class of mixing actions. Bibliography: 25 titles.
Keywords: measure preserving action, homogeneous spectrum, spectral multiplicity, weak closure of a subaction. 
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     author = {V. V. Ryzhikov},
     title = {Spectral multiplicities and asymptotic operator properties of actions with invariant measure},
     journal = {Sbornik. Mathematics},
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     number = {12},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2009_200_12_a4/}
}
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V. V. Ryzhikov. Spectral multiplicities and asymptotic operator properties of actions with invariant measure. Sbornik. Mathematics, Tome 200 (2009) no. 12, pp. 1833-1845. http://geodesic.mathdoc.fr/item/SM_2009_200_12_a4/