Scattering theory for the Laplacian on manifolds with bounded curvature

DOI10.1016/j.jfa.2007.06.001zbMath1133.58026arXivmath/0701298OpenAlexW2074498892MaRDI QIDQ2464870

Werner Müller, Gorm Salomonsen

Publication date: 17 December 2007

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0701298

zbMATH Keywords

Laplace operatorscattering theorymanifolds of bounded curvature

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Scattering theory for PDEs (35P25)

Related Items (11)

The BFK-gluing formula and relative determinants on manifolds with cusps ⋮ Asymptotics of relative heat traces and determinants on open surfaces of finite area ⋮ Sobolev theorems for cusp manifolds ⋮ Scattering theory without injectivity radius assumptions, and spectral stability for the Ricci flow ⋮ A GLUING FORMULA FOR THE ANALYTIC TORSION ON HYPERBOLIC MANIFOLDS WITH CUSPS ⋮ Equivalence of Sobolev spaces ⋮ Scattering the geometry of weighted graphs ⋮ On open scattering channels for manifolds with ends ⋮ On open scattering channels for a branched covering of the Euclidean plane ⋮ Scattering theory for the Hodge Laplacian ⋮ A geometric approach to the Landauer-Büttiker formula

Cites Work

• The analysis of linear partial differential operators. III: Pseudo-differential operators
• Manifolds with cusps of rank one. Spectral theory and \(L^ 2\)-index theorem
• Meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature
• Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds
• Phase space analysis of simple scattering systems: extensions of some work of Enss
• Analytic continuation of resolvent kernels on noncompact symmetric spaces
• Spaces of Riemannian metrics on open manifolds
• On the analytic continuation of rank one Eisenstein series
• Meromorphic families of compact operators
• Essential self-adjointness of powers of generators of hyperbolic equations
• Analytic continuation of the resolvent of the Laplacian on symmetric spaces of noncompact type
• Spectral Theory for Riemannian Manifolds with Cusps and a Related Trace Formula
• The Boundedness of Connection Coefficients and their Derivatives
• Riemannian geometry
• Equivalence of Sobolev spaces
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