TY - JOUR
T1 - Time-dependent scattering theory on manifolds
AU - Ito, K.
AU - Skibsted, E.
PY - 2019/9
Y1 - 2019/9
N2 - 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.
AB - 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.
KW - Long-range perturbation
KW - Riemannian manifold
KW - Scattering theory
KW - Schrödinger operator
UR - http://www.scopus.com/inward/record.url?scp=85066472658&partnerID=8YFLogxK
U2 - 10.1016/j.jfa.2019.05.016
DO - 10.1016/j.jfa.2019.05.016
M3 - Journal article
AN - SCOPUS:85066472658
SN - 0022-1236
VL - 277
SP - 1423
EP - 1468
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 5
ER -