Abstract.
This paper is a further development of complex methods in harmonic analysis on semi-simple Lie groups [AG], [BeR], [KrS1,2]. We study the growth behaviour of the holomorphic extension of the orbit map of the spherical vector of an irreducible spherical representation of a real reductive group G when approaching the boundary of the crown domain of the Riemannian symmetric space G/K. As an application, we prove that Maaß cusp forms have exponential decay.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Author information
Authors and Affiliations
Corresponding author
Additional information
During the preparation of this paper the second named author was partially supported by a Pionier Grant of the Netherlands Organization for Scientific Research (NWO). Part of this research was carried out in the fall of 2004, during which period both authors enjoyed the hospitality of the Research Institute for the Mathematical Sciences in Kyoto, Japan. It is our pleasure to thank the RIMS for its hospitality and for the stimulating environment it offers.
Received: August 2006, Revision: June 2007, Accepted: June 2007
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License ( https://creativecommons.org/licenses/by-nc/2.0 ), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Krötz, B., Opdam, E. Analysis on the Crown Domain. GAFA Geom. funct. anal. 18, 1326–1421 (2008). https://doi.org/10.1007/s00039-008-0684-5
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00039-008-0684-5