The residues of the resolvent on Damek-Ricci spaces
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- by R. J. Miatello and C. E. Will
- Proc. Amer. Math. Soc. 128 (2000), 1221-1229
- DOI: https://doi.org/10.1090/S0002-9939-99-05498-2
- Published electronically: October 18, 1999
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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.References
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Bibliographic Information
- R. J. Miatello
- Affiliation: Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, 5000 Córdoba, Argentina
- MR Author ID: 124160
- Email: miatello@mate.uncor.edu
- C. E. Will
- Affiliation: Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, 5000 Córdoba, Argentina
- MR Author ID: 649211
- Email: cwill@mate.uncor.edu
- 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
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 1221-1229
- MSC (1991): Primary 22E30
- DOI: https://doi.org/10.1090/S0002-9939-99-05498-2
- MathSciNet review: 1695119