Abstract:
This is a survey on harmonic analysis on real reductive Lie groups for the period 1950–1978. Contained is a description of the fundamental series of representations of a reductive group $G$, the theory of characters, a description of the Plancherel measure, a description of dual spaces with respect to the Fourier transform on $G$, the classification of irreducible representations of the group $G$, questions of harmonic analysis on symmetric spaces of noncompact type.
Citation:
D. P. Zhelobenko, “Harmonic analysis on reductive Lie groups”, Itogi Nauki i Tekhn. Ser. Mat. Anal., 17, VINITI, Moscow, 1979, 207–269; J. Soviet Math., 15:4 (1981), 490–529
\Bibitem{Zhe79}
\by D.~P.~Zhelobenko
\paper Harmonic analysis on reductive Lie groups
\serial Itogi Nauki i Tekhn. Ser. Mat. Anal.
\yr 1979
\vol 17
\pages 207--269
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/intm51}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=578771}
\zmath{https://zbmath.org/?q=an:0475.43008}
\transl
\jour J. Soviet Math.
\yr 1981
\vol 15
\issue 4
\pages 490--529
\crossref{https://doi.org/10.1007/BF01375564}
Linking options:
https://www.mathnet.ru/eng/intm51
https://www.mathnet.ru/eng/intm/v17/p207
This publication is cited in the following 2 articles:
P. A. Kuchment, “Spherical representation of solutions of invariant differential equations on a Riemannian symmetric space of noncompact type”, Math. USSR-Izv., 27:3 (1986), 535–548
D. V. Alekseevskii, “Lie groups”, J. Soviet Math., 28:6 (1985), 924–949
Citation in format AMSBIB
Contact us: