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Izv. RAN. Ser. Mat., 2002, Volume 66, Issue 1, Pages 167–202 (Mi izv376)  

This article is cited in 5 scientific papers (total in 5 papers)

Invariant subspaces in some function spaces on symmetric spaces. III

S. S. Platonov

Petrozavodsk State University

Abstract: We describe the structure of closed linear subspaces in some topological vector spaces that consist of functions on the exceptional non-compact symmetric space $M=F_4/{\operatorname{Spin}(9)}$ (the Cayley space) and are invariant under the natural quasi-regular representation of the group $F_4$. The class of function spaces under consideration contains the spaces $C^d(M)$ of $d$-times continuously differentiable functions ($d=0,1,…,\infty$) and the spaces of functions of exponential growth on $M$.

DOI: https://doi.org/10.4213/im376

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English version:
Izvestiya: Mathematics, 2002, 66:1, 165–200

Bibliographic databases:

UDC: 517.954
MSC: 43A85, 22E46
Received: 04.12.2000

Citation: S. S. Platonov, “Invariant subspaces in some function spaces on symmetric spaces. III”, Izv. RAN. Ser. Mat., 66:1 (2002), 167–202; Izv. Math., 66:1 (2002), 165–200

Citation in format AMSBIB
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\by S.~S.~Platonov
\paper Invariant subspaces in some function spaces on symmetric spaces.~III
\jour Izv. RAN. Ser. Mat.
\yr 2002
\vol 66
\issue 1
\pages 167--202
\mathnet{http://mi.mathnet.ru/izv376}
\crossref{https://doi.org/10.4213/im376}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1917542}
\zmath{https://zbmath.org/?q=an:1028.43014}
\transl
\jour Izv. Math.
\yr 2002
\vol 66
\issue 1
\pages 165--200
\crossref{https://doi.org/10.1070/IM2002v066n01ABEH000376}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-3543114517}


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    This publication is cited in the following articles:
    1. Platonov S.S., “On describing invariant subspaces of the space of smooth functions on a homogeneous manifold”, Acta Appl. Math., 81:1 (2004), 327–338  crossref  mathscinet  zmath  isi  elib  scopus
    2. Popov S.P., Tcheremissine F.G., “Subsonic rarefied gas flow over a rack of flat transverse plates”, Journal of Applied Mechanics and Technical Physics, 49:1 (2008), 46–52  crossref  zmath  adsnasa  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
    5. V. V. Volchkov, Vit. V. Volchkov, “Spectral synthesis on the group of conformal automorphisms of the unit disc”, Sb. Math., 209:1 (2018), 1–34  mathnet  crossref  crossref  adsnasa  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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