Time-dependent scattering theory on manifolds

K. Ito*, E. Skibsted

*Corresponding author for this work

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review


This is the third and the last paper in a series of papers on spectral and scattering theory for the Schrödinger operator on a manifold possessing an escape function, for example a manifold with asymptotically Euclidean and/or hyperbolic ends. Here we discuss the time-dependent scattering theory. A long-range perturbation is allowed, and scattering by obstacles, possibly non-smooth and/or unbounded in a certain way, is included in the theory. We also resolve a conjecture by Hempel–Post–Weder on cross-ends transmissions between two or more ends, formulated in a time-dependent manner.

Original languageEnglish
JournalJournal of Functional Analysis
Pages (from-to)1423-1468
Number of pages46
Publication statusPublished - Sept 2019


  • Long-range perturbation
  • Riemannian manifold
  • Scattering theory
  • Schrödinger operator


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