The residues of the resolvent on Damek-Ricci spaces

Miatello, R.; Will, C.

doi:10.1090/S0002-9939-99-05498-2

The residues of the resolvent on Damek-Ricci spaces
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by R. J. Miatello and C. E. Will PDF

Proc. Amer. Math. Soc. 128 (2000), 1221-1229 Request permission

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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