Eigenspaces of the Laplacian on hyperbolic spaces: Composition series and integral transforms
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Eigenspaces of the Laplacian on hyperbolic spaces : Composition series and integral transforms. / Schlichtkrull, Henrik.
I: Journal of Functional Analysis, Bind 70, Nr. 1, 01.1987, s. 194-219.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Eigenspaces of the Laplacian on hyperbolic spaces
T2 - Composition series and integral transforms
AU - Schlichtkrull, Henrik
N1 - Funding Information: * Partially supported by NSF grant DMS 80-01854 at Cornell University.
PY - 1987/1
Y1 - 1987/1
N2 - Let X be a projective real, complex, or quaternion hyperbolic space, realized as the pseudo-Riemannian symmetric space X ≅ G H with G = O(p, q), U(p, q), or Sp(p,q) (these are the classical isotropic symmetric spaces). Let Δ be the G-invariant Laplace-Beltrami operator on X. A complete description (by K-types), for each χ ∈ C, of all closed G-invariant subspaces of the eigenspace {f ∈ C∞(X)|Δf = χf} is given. The eigenspace representations are compared with principal series representations, using "Poisson-transformations". Similar results are obtained also for the exceptional isotropic symmetric space. The Langlands parameters of the spherical discrete series representations are determined.
AB - Let X be a projective real, complex, or quaternion hyperbolic space, realized as the pseudo-Riemannian symmetric space X ≅ G H with G = O(p, q), U(p, q), or Sp(p,q) (these are the classical isotropic symmetric spaces). Let Δ be the G-invariant Laplace-Beltrami operator on X. A complete description (by K-types), for each χ ∈ C, of all closed G-invariant subspaces of the eigenspace {f ∈ C∞(X)|Δf = χf} is given. The eigenspace representations are compared with principal series representations, using "Poisson-transformations". Similar results are obtained also for the exceptional isotropic symmetric space. The Langlands parameters of the spherical discrete series representations are determined.
UR - http://www.scopus.com/inward/record.url?scp=0011276711&partnerID=8YFLogxK
U2 - 10.1016/0022-1236(87)90130-3
DO - 10.1016/0022-1236(87)90130-3
M3 - Journal article
AN - SCOPUS:0011276711
VL - 70
SP - 194
EP - 219
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
IS - 1
ER -
ID: 304299135