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Mathematics of the USSR-Sbornik, 1975, Volume 27, Issue 1, Pages 51–65
DOI: https://doi.org/10.1070/SM1975v027n01ABEH002498
(Mi sm3670)
 

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

On unitary representations of the group of diffeomorphisms of the space $R^n$, $n\geqslant2$

R. S. Ismagilov
References:
Abstract: In this paper, one considers representations of the group $D^0(R^n)$, defined as the connected component of the identity in the group of all finitary diffeomorphisms of $R^n$, $n\geqslant2$, continuous with respect to natural convergence and containing a trivial subrepresentation of the subgroup $D_0^*(R^n)$, preserving volume in $R^n$. Under some additional assumptions there is a description of the irreducible unitary representations in Hilbert spaces. It is shown that each such representation is connected with some dynamical system by means of the standard construction of induced representations.
Bibliography: 5 titles.
Received: 20.11.1974
Russian version:
Matematicheskii Sbornik. Novaya Seriya, 1975, Volume 98(140), Number 1(9), Pages 55–71
Bibliographic databases:
UDC: 513.88
MSC: Primary 22A25, 28A65; Secondary 58D05
Language: English
Original paper language: Russian
Citation: R. S. Ismagilov, “On unitary representations of the group of diffeomorphisms of the space $R^n$, $n\geqslant2$”, Mat. Sb. (N.S.), 98(140):1(9) (1975), 55–71; Math. USSR-Sb., 27:1 (1975), 51–65
Citation in format AMSBIB
\Bibitem{Ism75}
\by R.~S.~Ismagilov
\paper On~unitary representations of the group of diffeomorphisms of the space $R^n$, $n\geqslant2$
\jour Mat. Sb. (N.S.)
\yr 1975
\vol 98(140)
\issue 1(9)
\pages 55--71
\mathnet{http://mi.mathnet.ru/sm3670}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=414795}
\zmath{https://zbmath.org/?q=an:0317.58008}
\transl
\jour Math. USSR-Sb.
\yr 1975
\vol 27
\issue 1
\pages 51--65
\crossref{https://doi.org/10.1070/SM1975v027n01ABEH002498}
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  • https://doi.org/10.1070/SM1975v027n01ABEH002498
  • https://www.mathnet.ru/eng/sm/v140/i1/p55
  • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics
    Statistics & downloads:
    Abstract page:393
    Russian version PDF:115
    English version PDF:9
    References:82
    First page:2
     
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