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Resonances for the Laplacian: the Cases BC2 and C2 (except SO0(p, 2) with p > 2 odd)

  • J. HilgertEmail author
  • A. Pasquale
  • T. Przebinda
Conference paper
Part of the Trends in Mathematics book series (TM)

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.

Keywords

Resonances resolvent Laplacian Riemannian symmetric spaces of the noncompact type direct products BC rank two 

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of MathematicsPaderborn UniversityPaderbornGermany
  2. 2.Université de LorraineInstitut Elie Cartan de LorraineMetzFrance
  3. 3.Department of MathematicsUniversity of OklahomaNorman, OKUSA

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