Abstract
In the present Chapter we give applications and finer points of the spectral theory of the Laplace-Beltrami operator Δ on L2(Γ\IH) in case Γ < PSL(2, ℂ) is a discrete cocompact group. We already know from the preceding Chapter that —Δ is essentially self-adjoint and positive on the subspace D ⊂ L2 (Γ\IH) consisting of all C 2-functions f ⋵ L 2(Γ\IH) such that Δf ∈ L 2 (Γ\IH) . This means that the closure of the graph of Δ in L 2 (Γ\IH) × L 2 (Γ\IH) is the graph of a self-adjoint linear operator \(\tilde \Delta :\tilde D \to {L^2}(\Gamma \backslash IH)\)
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© 1998 Springer-Verlag Berlin Heidelberg
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Elstrodt, J., Grunewald, F., Mennicke, J. (1998). Spectral Theory of the Laplace Operator for Cocompact Groups. In: Groups Acting on Hyperbolic Space. Springer Monographs in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03626-6_5
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DOI: https://doi.org/10.1007/978-3-662-03626-6_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08302-0
Online ISBN: 978-3-662-03626-6
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