caa a22 4500 388046678 CHVBK 20180307125040.0 cr unu---uuuuu 161130e199810 xx s 000 0 eng 10.1017/S1446788700034959 doi S1446788700034959 pii (NATIONALLICENCE)cambridge-10.1017/S1446788700034959 Lipsman Ronald L. Department of Mathematics, University of Maryland, College Park, MD 20742 USA e-mail: rll@math.umd.edu The Plancherel formula for the horocycle spaces and generalizations, II [Elektronische Daten] [Ronald L. Lipsman] The Plancherel formula for various semisimple homogeneous spaces with non-reductive stability group is derived within the framework of the Bonnet Plancherel formula for the direct integral decomposition of a quasi-regular representation. These formulas represent a continuation of the author's program to establish a new paradigm for concrete Plancherel analysis on homogeneous spaces wherein the distinction between finite and infinite multiplicity is de-emphasized. One interesting feature of the paper is the computation of the Bonnet nuclear operators corresponding to certain exponential representations (roughly those induced from infinite-dimensional representations of a subgroup). Another feature is a natural realization of the direct integral decomposition over a canonical set of concrete irreducible representations, rather than over the unitary dual. Copyright © Australian Mathematical Society 1998 primary 22E46 nationallicence secondary 22E45 nationallicence Journal of the Australian Mathematical Society Cambridge University Press 65/2(1998-10), 194-211 1446-7887 65:2<194 1998 65 JAZ https://doi.org/10.1017/S1446788700034959 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S1446788700034959 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Lipsman Ronald L. Department of Mathematics, University of Maryland, College Park, MD 20742 USA e-mail: rll@math.umd.edu NATIONALLICENCE 773 0- Journal of the Australian Mathematical Society Cambridge University Press 65/2(1998-10), 194-211 1446-7887 65:2<194 1998 65 JAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence SWISSBIB 387756000 BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge