Scattering theory for Schrödinger equations on manifolds with asymptotically polynomially growing ends

2011/12/21 by Shinichiro Itozaki, Itozaki, Shinichiro
Mathematics · #35P25 #58J50 #81U05 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1112.5135

openalex publication_date 2011/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a time-dependent scattering theory for Schrödinger operators on a manifold with asymptotically polynomially growing ends. We use the Mourre theory to show the spectral properties of self-adjoint second-order elliptic operators. We prove the existence and the asymptotic completeness of wave operators using the smooth perturbation theory of Kato. We also consider a two-space scattering with a simple reference system.

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