The Laplace operator on hyperbolic three manifolds with cusps of non- maximal rank
type: Item
instance of: scholarly article
title: The Laplace operator on hyperbolic three manifolds with cusps of non- maximal rank
zbMATH Open document ID: 0763.58028
DOI: 10.1007/BF01243915
author: Peter D. Hislop
author: Richard Froese
author: Peter Perry
published in: Inventiones Mathematicae
publication date: 1992-09-27T00:00:00Z
full work available at URL: https://eudml.org/doc/143944
review text: The generalized eigenfunction expansion for the Laplace operator on a hyperbolic 3-manifold \(M=\mathbb{H}/\Gamma\) is studied, where \(\Gamma\) is a geometrically finite discrete group of orientation preserving isometries, which may contain parabolic elements of non-maximal rank. The existence of a continuum eigenfunction expansion is proved and it is shown that in the spectral parameter the eigenfunctions (Eisenstein series for \(\Gamma)\) have meromorphic continuations to \(\mathbb{C}\backslash\{1\}\).
Mathematics Subject Classification ID: 58J50
Mathematics Subject Classification ID: 11F72
zbMATH DE Number: 59804
zbMATH Keywords: Eisenstein series
zbMATH Keywords: Laplace operator
zbMATH Keywords: hyperbolic 3-manifold
zbMATH Keywords: eigenfunction expansion
reviewed by: Helga Baum
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 59804