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Izv. RAN. Ser. Mat., 1998, Volume 62, Issue 2, Pages 131–168 (Mi izv178)  

This article is cited in 4 scientific papers (total in 4 papers)

Invariant subspaces in some function spaces on symmetric spaces. II

S. S. Platonov

Petrozavodsk State University

Abstract: Let $G$ be a semisimple connected Lie group with finite centre, $K$ a maximal compact subgroup of $G$, and $M=G/K$ a Riemannian symmetric space of non-compact type. We study the problem of describing the structure of closed linear subspaces in various function spaces on $M$ that are invariant under the quasiregular representation of the group $G$. We consider the case when $M$ is a symplectic symmetric space of rank 1.

DOI: https://doi.org/10.4213/im178

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English version:
Izvestiya: Mathematics, 1998, 62:2, 339–374

Bibliographic databases:

MSC: 43A85, 22E46
Received: 25.01.1996

Citation: S. S. Platonov, “Invariant subspaces in some function spaces on symmetric spaces. II”, Izv. RAN. Ser. Mat., 62:2 (1998), 131–168; Izv. Math., 62:2 (1998), 339–374

Citation in format AMSBIB
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\pages 131--168
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\pages 339--374
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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. III”, Izv. Math., 66:1 (2002), 165–200  mathnet  crossref  crossref  mathscinet  zmath
    2. 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  scopus
    3. 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
    4. 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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