The Laplace operator on a hyperbolic manifold. I: Spectral and scattering theory (Q1094722)

Using techniques of stationary scattering theory for the Schrödinger equation, the author proves the absence of the singular spectrum and obtains incoming and outgoing spectral representations for the Laplace- Beltrami operator on manifolds \(M_ n\) arising as the quotient of hyperbolic n-dimensional space by a geometrically finite, discrete group of hyperbolic isometries.