THE PLANCHEREL FORMULA FOR THE HOROCYCLE SPACE AND GENERALIZATIONS

Authors
LIPSMAN RL
Citation
Rl. Lipsman, THE PLANCHEREL FORMULA FOR THE HOROCYCLE SPACE AND GENERALIZATIONS, Journal of the Australian Mathematical Society. Series A. Pure mathematics and statistics, 61, 1996, pp. 42-56
Citations number
10
Categorie Soggetti
Mathematics, General","Statistic & Probability",Mathematics,"Statistic & Probability
Journal title
Journal of the Australian Mathematical Society. Series A. Pure mathematics and statistics → ACNP
ISSN journal
02636115
Volume
61
Year of publication
1996
Part
1
Pages
42 - 56
Database
ISI
SICI code
0263-6115(1996)61:<42:TPFFTH>2.0.ZU;2-G
Abstract
The Plancherel formula for the horocycle space, and several generaliza tions, is derived within the framework of quasi-regular representation s which have monomial spectrum. The proof uses only machinery from the Penney-Fujiwara distribution-theoretic technique; no special semisimp le harmonic analysis is needed. The Plancherel formulas obtained inclu de the spectral distributions and the intertwining operators that effe ct the direct integral decomposition of the quasi-regular representati on.