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Izv. Akad. Nauk SSSR Ser. Mat., 1976, Volume 40, Issue 3, Pages 562–592 (Mi izv2142)  

This article is cited in 7 scientific papers (total in 7 papers)

Harmonic analysis on Riemannian symmetric spaces of negative curvature and scattering theory

M. A. Semenov-Tian-Shansky


Abstract: Harmonic analysis on a Riemannian symmetric space can be connected with the study of a nonstationary system of equations that has been constructed with respect to the ring of Laplace operators. The scattering theory for this system generalizes the scattering theory for hyperbolic equations constructed by Lax and Phillips. The paper contains a series of new spectral theorems generalizing the Harish–Chandra theorem and a formulation of a causality principle for scattering operators.
Bibliography: 23 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1976, 10:3, 535–563

Bibliographic databases:

UDC: 512.4+513.83
MSC: Primary 43A85; Secondary 35P25
Received: 23.12.1974

Citation: M. A. Semenov-Tian-Shansky, “Harmonic analysis on Riemannian symmetric spaces of negative curvature and scattering theory”, Izv. Akad. Nauk SSSR Ser. Mat., 40:3 (1976), 562–592; Math. USSR-Izv., 10:3 (1976), 535–563

Citation in format AMSBIB
\Bibitem{Sem76}
\by M.~A.~Semenov-Tian-Shansky
\paper Harmonic analysis on Riemannian symmetric spaces of negative curvature and
scattering theory
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1976
\vol 40
\issue 3
\pages 562--592
\mathnet{http://mi.mathnet.ru/izv2142}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=467179}
\zmath{https://zbmath.org/?q=an:0354.35071}
\transl
\jour Math. USSR-Izv.
\yr 1976
\vol 10
\issue 3
\pages 535--563
\crossref{https://doi.org/10.1070/IM1976v010n03ABEH001717}


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    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. Peter D. Lax, Ralph S. Phillips, “Translation representations for the solution of the non-euclidean wave equation”, Comm Pure Appl Math, 32:5 (1979), 617  crossref  mathscinet  zmath
    2. V. A. Zolotarev, “The Lax–Phillips scattering scheme on groups, and a functional model of a Lie algebra”, Russian Acad. Sci. Sb. Math., 76:1 (1993), 99–122  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. Yu. Yu. Berest, A. P. Veselov, “Huygens' principle and integrability”, Russian Math. Surveys, 49:6 (1994), 5–77  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. V. A. Zolotarev, “A functional model for the Lie algebra $\operatorname{ISO}(1,1)$ of linear non-self-adjoint operators”, Sb. Math., 186:1 (1995), 79–106  mathnet  crossref  mathscinet  zmath  isi
    5. S. P. Khekalo, “Solution of the Hadamard problem in the class of stepwise gauge-equivalent deformations of homogeneous differential operators with constant coefficients”, St. Petersburg Math. J., 19:6 (2008), 1015–1028  mathnet  crossref  mathscinet  zmath  isi  elib
    6. A. Yu. Morozov, “Unitary integrals and related matrix models”, Theoret. and Math. Phys., 162:1 (2010), 1–33  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. A. S. Anokhina, A. A. Morozov, “Cabling procedure for the colored HOMFLY polynomials”, Theoret. and Math. Phys., 178:1 (2014), 1–58  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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