RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Zametki, 2000, Volume 68, Issue 5, Pages 643–647 (Mi mz985)  

This article is cited in 10 scientific papers (total in 10 papers)

On the Spectrum of Cartesian Powers of Classical Automorphisms

O. N. Ageev

N. E. Bauman Moscow State Technical University

Abstract: We prove the following statement: the set of all essential spectral multiplicities of $T^{(n)}=T\times…\times T$($n$ times) is $\{n,n(n-1),…,n!\}$ on $\{\operatorname{const}\}^\perp$ for Chacon transformations $T$, or, equivalently, the operator $T^{(n)}$ has a simple spectrum on the subspace $C_{\operatorname{sim}}$ 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 $T\times T$ has a homogeneous spectrum of multiplicity 2 on $\{\operatorname{const}\}^\perp$, i.e., this is a solution of Rokhlin"s problem for Chacon transformations. Similar statements are considered for other classical automorphisms.

DOI: https://doi.org/10.4213/mzm985

Full text: PDF file (193 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 2000, 68:5, 547–551

Bibliographic databases:

UDC: 517.9
Received: 31.01.2000

Citation: O. N. Ageev, “On the Spectrum of Cartesian Powers of Classical Automorphisms”, Mat. Zametki, 68:5 (2000), 643–647; Math. Notes, 68:5 (2000), 547–551

Citation in format AMSBIB
\Bibitem{Age00}
\by O.~N.~Ageev
\paper On the Spectrum of Cartesian Powers of Classical Automorphisms
\jour Mat. Zametki
\yr 2000
\vol 68
\issue 5
\pages 643--647
\mathnet{http://mi.mathnet.ru/mz985}
\crossref{https://doi.org/10.4213/mzm985}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1835446}
\zmath{https://zbmath.org/?q=an:1042.37003}
\transl
\jour Math. Notes
\yr 2000
\vol 68
\issue 5
\pages 547--551
\crossref{https://doi.org/10.1023/A:1026698921311}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000166684000001}


Linking options:
  • http://mi.mathnet.ru/eng/mz985
  • https://doi.org/10.4213/mzm985
  • http://mi.mathnet.ru/eng/mz/v68/i5/p643

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. D. V. Anosov, “Spectral Multiplicity in Ergodic Theory”, Proc. Steklov Inst. Math., 290, suppl. 1 (2015), 1–44  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. Ageev, ON, “On asymmetry of the future and the past for limit self-joinings”, Proceedings of the American Mathematical Society, 131:7 (2003), 2053  crossref  mathscinet  zmath  isi  scopus
    3. Danilenko, AI, “Explicit solution of Rokhlin's problem on homogeneous spectrum and applications”, Ergodic Theory and Dynamical Systems, 26 (2006), 1467  crossref  mathscinet  zmath  isi  scopus
    4. Ageev, O, “Mixing with staircase multiplicity functions”, Ergodic Theory and Dynamical Systems, 28 (2008), 1687  crossref  mathscinet  zmath  isi  scopus
    5. Danilenko A.I., “(C, F)-Actions in Ergodic Theory”, In Memory of Alexander Reznikov, Progress in Mathematics, 265, eds. Kapranov M., Kolyada S., Manin Y., Moree P., Potyagailo L., Birkhauser Verlag Ag, 2008, 325–351  crossref  mathscinet  zmath  isi  scopus  scopus
    6. Roy, E, “Poisson suspensions and infinite ergodic theory”, Ergodic Theory and Dynamical Systems, 29 (2009), 667  crossref  mathscinet  zmath  isi  scopus
    7. Katok A., Lemanczyk M., “Some new cases of realization of spectral multiplicity function for ergodic transformations”, Fundamenta Mathematicae, 206 (2009), 185–215  crossref  mathscinet  zmath  isi  elib  scopus
    8. Lemanczyk M., Parreau F., Roy E., “Joining Primeness and Disjointness From Infinitely Divisible Systems”, Proc. Amer. Math. Soc., 139:1 (2011), 185–199  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    9. Kulaga-Przymus J., Parreau F., “Disjointness Properties for Cartesian Products of Weakly Mixing Systems”, Colloq. Math., 128:2 (2012), 153–177  crossref  mathscinet  zmath  isi  elib  scopus
    10. Danilenko A.I., “A Survey on Spectral Multiplicities of Ergodic Actions”, Ergod. Theory Dyn. Syst., 33:Part 1 (2013), 81–117  crossref  mathscinet  zmath  isi  elib  scopus
  • Математические заметки Mathematical Notes
    Number of views:
    This page:219
    Full text:103
    References:45
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020