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- W2014992531 abstract "Let $Gamma$ be a discrete subgroup of automorphisms of ${{mathbf {H}}^n}$, with fundamental polyhedron of finite volume, finite number of sides, and $N$ cusps. Denote by ${Delta _Gamma }$ the Laplace-Beltrami operator acting on functions automorphic with respect to $Gamma$. We give a new short proof of the fact that ${Delta _Gamma }$ has absolutely continuous spectrum of uniform multiplicity $N$ on $( - infty ,{((n - 1)/2)^2})$, plus a standard discrete spectrum. We show that this property of the spectrum is unchanged under arbitrary perturbation of the metric on a compact set. Our method avoids Eisenstein series entirely and proceeds instead by constructing explicitly a translation representation for the associated wave equation." @default.
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- W2014992531 date "1985-02-01" @default.
- W2014992531 modified "2023-10-05" @default.
- W2014992531 title "Translation representations for automorphic solutions of the wave equation in non-Euclidean spaces; the case of finite volume" @default.
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- W2014992531 doi "https://doi.org/10.1090/s0002-9947-1985-0784011-9" @default.
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