TY - JOUR
T1 - Cuspidal integrals for SL(3)∕Kϵ
AU - Flensted-Jensen, Mogens
AU - Kuit, Job J.
PY - 2018
Y1 - 2018
N2 - We show that for the symmetric spaces SL(3,R)∕SO(1,2)e and SL(3,C)∕SU(1,2) the cuspidal integrals are absolutely convergent. We further determine the behavior of the corresponding Radon transforms and relate the kernels of the Radon transforms to the different series of representations occurring in the Plancherel decomposition of these spaces. Finally we show that for the symmetric space SL(3,H)∕Sp(1,2) the cuspidal integrals are not convergent for all Schwartz functions.
AB - We show that for the symmetric spaces SL(3,R)∕SO(1,2)e and SL(3,C)∕SU(1,2) the cuspidal integrals are absolutely convergent. We further determine the behavior of the corresponding Radon transforms and relate the kernels of the Radon transforms to the different series of representations occurring in the Plancherel decomposition of these spaces. Finally we show that for the symmetric space SL(3,H)∕Sp(1,2) the cuspidal integrals are not convergent for all Schwartz functions.
UR - http://www.scopus.com/inward/record.url?scp=85047988629&partnerID=8YFLogxK
U2 - 10.1016/j.indag.2018.05.005
DO - 10.1016/j.indag.2018.05.005
M3 - Journal article
AN - SCOPUS:85047988629
SN - 0019-3577
VL - 29
SP - 1235
EP - 1258
JO - Indagationes Mathematicae
JF - Indagationes Mathematicae
IS - 5
ER -