Spectral multiplicities and asymptotic operator properties of actions with invariant measure
- M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)
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 {l_brace}p,q,pq{r_brace}, {l_brace}p,q,r,pq,pr,rq,pqr{r_brace} 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.
- OSTI ID:
- 21301249
- Journal Information:
- Sbornik. Mathematics, Vol. 200, Issue 12; Other Information: DOI: 10.1070/SM2009v200n12ABEH004061; Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
- Country of Publication:
- United States
- Language:
- English
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