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The Plancherel formula for the horocycle space and generalizations

Part of: Abstract harmonic analysis Lie groups

Published online by Cambridge University Press:  09 April 2009

Ronald L. Lipsman
Ronald L. Lipsman
Affiliation:
Department of Mathematics University of MarylandCollege Park, Maryland 20742, USA
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Abstract

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The Plancherel formula for the horocycle space, and several generalizations, is derived within the framework of quasi-regular representations which have monomial spectrum. The proof uses only machinery from the Penney-Fujiwara distribution-theoretic technique; no special semisimple harmonic analysis is needed. The Plancherel formulas obtained include the spectral distributions and the intertwining operators that effect the direct integral decomposition of the quasi-regular representation.

MSC classification

Secondary: 22E46: Semisimple Lie groups and their representations 43A85: Analysis on homogeneous spaces
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 61 , Issue 1 , August 1996 , pp. 42 - 56
Copyright
Copyright © Australian Mathematical Society 1996

References

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