LP Spectral Theory of Kleinian Groups
نویسندگان
چکیده
Let r be a geometrically finite group acting on the hyperbolic space HN+’ and let H, denote the Laplace-Beltrami operator on M = T\H”‘+ ‘, which we assume is not compact. If M is either of finite volume or cusp-free, we determine completely the Lp spectrum of Hr for 1 $ p -C co, tinding that it depends upon p in a nontrivial manner. We also obtain a number of pointwise and Lp decay properties of the Lz eigenfunctions associated with eigenvalues E in the range 0 < EC N2/4. Cl 1988 Academic Press, Inc.
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