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Harmonic analysis on non-semisimple symmetric spaces

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Abstract

It is proven that theL 2 spectrum for certain non-semisimple, non-nilpotent symmetric spaces is multiplicity-free. The spectrum and spectral measure are computed precisely for symmetric spaces corresponding to non-compact motion groups. Somewhat less complete results on theL 2 spectrum — in both the Mackey Machine and Orbit Method modes — are given for general semidirect product symmetric spaces.

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Authors and Affiliations

  1. Department of Mathematics, University of Maryland, 20742, College Park, MD, USA

    Ronald L. Lipsman

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  1. Ronald L. Lipsman
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Additional information

The author was supported by the NSF through DMS84-00900-A01 and by a Senior Fulbright Fellowship.

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Lipsman, R.L. Harmonic analysis on non-semisimple symmetric spaces. Israel J. Math. 54, 335–350 (1986). https://doi.org/10.1007/BF02764962

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  • DOI: https://doi.org/10.1007/BF02764962

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