An application of scattering theory to the spectrum of the Laplace-Beltrami operator

2003/01/10 by Francesca Antoci
Mathematics · #math.SP #math.DG #msc:58J50

paper · pdf

published as Rend. Acad. Naz. Sci. XL Mem. Math. Appl.(2001) Vol. XXV Fasc.1, 97-109 · 13 pages

arxiv created 2003/01/10 · arxiv updated 2009/11/30

Abstract

Applying a theorem due to Belopol'ski and Birman, we show that the Laplace-Beltrami operator on 1-forms on \bf Rⁿ endowed with an asymptotically Euclidean metric has absolutely continuous spectrum equal to [0, +∞).

Related

• Scattering theory for Riemannian Laplacians
• On the absolutely continuous spectrum of the Laplace-Beltrami operator acting on p-forms for a class of warped product metrics
• On the spectrum of the Laplace-Beltrami operator for p-forms on asymptotically hyperbolic manifolds
• The Zero-in-the-Spectrum Question
• Geometric and Obstacle Scattering at Low Energy