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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The residues of the resolvent
on Damek-Ricci spaces


Authors: R. J. Miatello and C. E. Will
Journal: Proc. Amer. Math. Soc. 128 (2000), 1221-1229
MSC (1991): Primary 22E30
Published electronically: October 18, 1999
MathSciNet review: 1695119
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Abstract | References | Similar Articles | Additional Information

Abstract: We determine the poles and residues of the resolvent kernel of the Laplacian on a Damek-Ricci space $S.$ We show that all poles are simple and the residues define convolution operators of finite rank. This generalizes a result of Guillopé-Zworski for the real hyperbolic $n$-space. If $S$ corresponds to a symmetric space of negative curvature $G/K$, the image of each residue is a ${\frak g}_c$-module with a specific highest weight. We compute the dimension by the Weyl dimension formula.


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Additional Information

R. J. Miatello
Affiliation: Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, 5000 Córdoba, Argentina
Email: miatello@mate.uncor.edu

C. E. Will
Affiliation: Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, 5000 Córdoba, Argentina
Email: cwill@mate.uncor.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05498-2
PII: S 0002-9939(99)05498-2
Received by editor(s): May 27, 1998
Published electronically: October 18, 1999
Additional Notes: This research was partially supported by Conicet, Conicor, SecytUNC (Córdoba), and I.C.T.P. (Trieste)
Communicated by: Roe Goodman
Article copyright: © Copyright 2000 American Mathematical Society