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Time-dependent scattering theory on manifolds
- Source :
- Ito, K & Skibsted, E 2019, ' Time-dependent scattering theory on manifolds ', Journal of Functional Analysis, vol. 277, no. 5, pp. 1423-1468 . https://doi.org/10.1016/j.jfa.2019.05.016
- Publication Year :
- 2019
- Publisher :
- Elsevier BV, 2019.
-
Abstract
- This is the third and the last paper in a series of papers on spectral and scattering theory for the Schrodinger 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.
- Subjects :
- Mathematics - Differential Geometry
Scattering theory
Perturbation (astronomy)
01 natural sciences
symbols.namesake
Mathematics - Analysis of PDEs
0103 physical sciences
Euclidean geometry
FOS: Mathematics
0101 mathematics
Mathematical physics
Mathematics
Schrödinger operator
Long-range perturbation
Conjecture
Riemannian manifold
Scattering
010102 general mathematics
Manifold
Differential Geometry (math.DG)
symbols
010307 mathematical physics
Analysis
Schrödinger's cat
Analysis of PDEs (math.AP)
Subjects
Details
- ISSN :
- 00221236
- Volume :
- 277
- Database :
- OpenAIRE
- Journal :
- Journal of Functional Analysis
- Accession number :
- edsair.doi.dedup.....443df33b1980aae79efcd1c2092be5d0