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Harmonic analysis on reductive Lie groups

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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.

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  1. D. P. Zhelobenko
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Translated from Itogi Nauki i Tekhniki, Matematicheskii Analiz, Vol. 17, pp. 207–269, 1979.

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Zhelobenko, D.P. Harmonic analysis on reductive Lie groups. J Math Sci 15, 490–529 (1981). https://doi.org/10.1007/BF01375564

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