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Izv. RAN. Ser. Mat., 1995, Volume 59, Issue 5, Pages 127–172 (Mi izv46)  

This article is cited in 6 scientific papers (total in 6 papers)

Invariant subspaces of some function spaces on symmetric spaces. I

S. S. Platonov

Petrozavodsk State University

Abstract: The article describes the construction of closed linear subspaces of some function spaces on the symmetric space $M=\operatorname{SU}(n,1)/U(n)$ that are invariant with respect to the natural quasiregular representation of the group $\operatorname{SU}(n,1)$. The function spaces considered include, in particular, the spaces $C^d(M)$ $(d=0,1,…,\infty)$ and spaces of functions of exponential growth on $M$.

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English version:
Izvestiya: Mathematics, 1995, 59:5, 1007–1050

Bibliographic databases:

MSC: Primary 22E30, 22E46, 43A85; Secondary 43A45, 53C35
Received: 13.05.1994

Citation: S. S. Platonov, “Invariant subspaces of some function spaces on symmetric spaces. I”, Izv. RAN. Ser. Mat., 59:5 (1995), 127–172; Izv. Math., 59:5 (1995), 1007–1050

Citation in format AMSBIB
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\by S.~S.~Platonov
\paper Invariant subspaces of some function spaces on symmetric spaces.~I
\jour Izv. RAN. Ser. Mat.
\yr 1995
\vol 59
\issue 5
\pages 127--172
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1360639}
\zmath{https://zbmath.org/?q=an:0879.43004}
\transl
\jour Izv. Math.
\yr 1995
\vol 59
\issue 5
\pages 1007--1050
\crossref{https://doi.org/10.1070/IM1995v059n05ABEH000046}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995UH54100009}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. S. Platonov, “Invariant subspaces in some function spaces on symmetric spaces. II”, Izv. Math., 62:2 (1998), 339–374  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. S. S. Platonov, “Invariant subspaces in some function spaces on symmetric spaces. III”, Izv. Math., 66:1 (2002), 165–200  mathnet  crossref  crossref  mathscinet  zmath
    3. Platonov S.S., “On describing invariant subspaces of the space of smooth functions on a homogeneous manifold”, Acta Applicandae Mathematicae, 81:1 (2004), 327–338  crossref  mathscinet  zmath  isi  elib
    4. Andreichenko D.K., Andreichenko K.P., Petrova T.Y., “Dynamic modelling of a non-conservative discrete-continuous system”, Pmm Journal of Applied Mathematics and Mechanics, 68:5 (2004), 691–698  crossref  isi
    5. S. S. Platonov, “Invariantnye podprostranstva v funktsionalnykh prostranstvakh medlennogo rosta na svetovom konuse v $R^{3}$”, Trudy PGU. Matematika, 2011, no. 18, 21–60  mathnet  mathscinet
    6. S. S. Platonov, “Invariant subspaces in some function spaces on the light cone in $\mathbb R^3$”, Sb. Math., 203:6 (2012), 864–892  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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