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Izv. Akad. Nauk SSSR Ser. Mat., 1969, Volume 33, Issue 5, Pages 931–973 (Mi izv2188)  

This article is cited in 8 scientific papers (total in 9 papers)

Operational calculus on a complex semisimple Lie group

D. P. Zhelobenko


Abstract: For every complex semisimple Lie algebra $\mathfrak g$ we construct a so-called operational calculus, which consists in the isomorphic embedding of $\mathfrak g$ along with its associative hull $\mathfrak G$ into a certain algebra of operator polynomials. We investigate the image of $\mathfrak G$ under this embedding; the resulting theorems comprise the algebraic analog of the functional duality theorems of harmonic analysis (theorems of Paley–Wiener type).

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English version:
Mathematics of the USSR-Izvestiya, 1969, 3:5, 881–916

Bibliographic databases:

UDC: 519.4
MSC: 22E46, 22E30, 44A40
Received: 23.01.1969

Citation: D. P. Zhelobenko, “Operational calculus on a complex semisimple Lie group”, Izv. Akad. Nauk SSSR Ser. Mat., 33:5 (1969), 931–973; Math. USSR-Izv., 3:5 (1969), 881–916

Citation in format AMSBIB
\Bibitem{Zhe69}
\by D.~P.~Zhelobenko
\paper Operational calculus on a~complex semisimple Lie group
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1969
\vol 33
\issue 5
\pages 931--973
\mathnet{http://mi.mathnet.ru/izv2188}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=262420}
\zmath{https://zbmath.org/?q=an:0218.17006}
\transl
\jour Math. USSR-Izv.
\yr 1969
\vol 3
\issue 5
\pages 881--916
\crossref{https://doi.org/10.1070/IM1969v003n05ABEH000809}


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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. D. P. Zhelobenko, “Harmonic analysis of functions on semisimple Lie groups. II”, Math. USSR-Izv., 3:6 (1969), 1183–1217  mathnet  crossref  mathscinet  zmath
    2. D. P. Zhelobenko, M. A. Naimark, “Description of the completely irreducible representations of a complex semisimple Lie group”, Math. USSR-Izv., 4:1 (1970), 59–83  mathnet  crossref  mathscinet  zmath
    3. D. P. Zhelobenko, “On the irreducible representations of a complex semisimple Lie group”, Funct. Anal. Appl., 4:2 (1970), 163–165  mathnet  crossref  mathscinet  zmath
    4. D. P. Zhelobenko, “Classification of extremally irreducible and normally irreducible representations of semisimple complex connected Lie groups”, Math. USSR-Izv., 5:3 (1971), 589–613  mathnet  crossref  mathscinet  zmath
    5. D. P. Zhelobenko, “Cyclic modules for a complex semisimple Lie group”, Math. USSR-Izv., 7:3 (1973), 497–510  mathnet  crossref  mathscinet  zmath
    6. A. I. Fomin, “Quasisimple irreducible representations of the group $SL(3,\mathbb{R})$”, Funct. Anal. Appl., 9:3 (1975), 237–243  mathnet  crossref  mathscinet  zmath
    7. P Torasso, “Le Théorème de Paley-Wiener pour l'espace des fonctions indéfiniment différentiables et à support compact sur un espace symétrique de type non-compact”, Journal of Functional Analysis, 26:2 (1977), 201  crossref
    8. Kenneth D. Johnson, “Paley-Wiener theorems on groups of split rank one”, Journal of Functional Analysis, 34:1 (1979), 54  crossref
    9. Yu. A. Neretin, S. M. Khoroshkin, “Mathematical works of D. P. Zhelobenko”, Russian Math. Surveys, 64:1 (2009), 187–198  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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