Abstract
Let X = G/K be a Riemannian symmetric space of the noncompact type and restricted root system BC2 or C2 (except for G = SO0(p, 2) with p > 2 odd). The analysis of the meromorphic continuation of the resolvent of the Laplacian of X is reduced from the analysis of the same problem for a direct product of two isomorphic rank-one Riemannian symmetric spaces of the noncompact type which are not isomorphic to real hyperbolic spaces. We prove that the resolvent of the Laplacian of X can be lifted to a meromorphic function on a Riemann surface which is a branched covering of the complex plane. Its poles, that is the resonances of the Laplacian, are explicitly located on this Riemann surface. The residue operators at the resonances have finite rank. Their images are finite direct sums of finite-dimensional irreducible spherical representations of G.
Mathematics Subject Classification (2010). Primary: 43A85; secondary: 58J50, 22E30.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Hilgert, J., Pasquale, A., Przebinda, T. (2016). Resonances for the Laplacian: the Cases BC2 and C2 (except SO0(p, 2) with p > 2 odd). In: Kielanowski, P., Ali, S., Bieliavsky, P., Odzijewicz, A., Schlichenmaier, M., Voronov, T. (eds) Geometric Methods in Physics. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-31756-4_15
Download citation
DOI: https://doi.org/10.1007/978-3-319-31756-4_15
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-31755-7
Online ISBN: 978-3-319-31756-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)