The Laplace operator on a hyperbolic manifold I. Spectral and scattering theory |
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Institution: | Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506 USA |
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Abstract: | Using techniques of stationary scattering theory for the Schrödinger equation, we show absence of singular spectrum and obtain incoming and outgoing spectral representations for the Laplace-Beltrami operator on manifolds Mn arising as the quotient of hyperbolic n-dimensional space by a geometrically finite, discrete group of hyperbolic isometries. We consider manifolds Mn of infinite volume. In subsequent papers, we will use the techniques developed here to analytically continue Eisenstein series for a large class of discrete groups, including some groups with parabolic elements. |
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