TY - JOUR
T1 - The Constant Term of Tempered Functions on a Real Spherical Space
AU - Delorme, Patrick
AU - Krötz, Bernhard
AU - Souaifi, Sofiane
AU - Beuzart-Plessis, Raphaël
N1 - Publisher Copyright:
© 2021 The Author(s). Published by Oxford University Press. All rights reserved.
PY - 2022/6/1
Y1 - 2022/6/1
N2 - Let Z be a unimodular real spherical space. We develop a theory of constant terms for tempered functions on Z, which parallels the work of Harish-Chandra. The constant terms fI of an eigenfunction f are parametrized by subsets I of the set S of spherical roots that determine the fine geometry of Z at infinity. Constant terms are transitive i.e., (fJ)I=fI for I⊂ J, and our main result is a quantitative bound of the difference f-fI, which is uniform in the parameter of the eigenfunction.
AB - Let Z be a unimodular real spherical space. We develop a theory of constant terms for tempered functions on Z, which parallels the work of Harish-Chandra. The constant terms fI of an eigenfunction f are parametrized by subsets I of the set S of spherical roots that determine the fine geometry of Z at infinity. Constant terms are transitive i.e., (fJ)I=fI for I⊂ J, and our main result is a quantitative bound of the difference f-fI, which is uniform in the parameter of the eigenfunction.
UR - https://www.scopus.com/pages/publications/85132879768
U2 - 10.1093/imrn/rnaa395
DO - 10.1093/imrn/rnaa395
M3 - Article
AN - SCOPUS:85132879768
SN - 1073-7928
VL - 2022
SP - 9413
EP - 9498
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
IS - 12
ER -