Threshold between short and long-range potentials for non-local Schr\"odinger operators
Mathematical Physics
2020-05-27 v1 math.MP
Abstract
We develop scattering theory for non-local Schr\"odinger operators defined by functions of the Laplacian that include its fractional power with . In particular, our function belongs to a wider class than the set of Bernstein functions. By showing the existence and non-existence of the wave operators, we clarify the threshold between the short and long-range decay conditions for perturbational potentials.
Cite
@article{arxiv.2005.12711,
title = {Threshold between short and long-range potentials for non-local Schr\"odinger operators},
author = {Atsuhide Ishida and Kazuyuki Wada},
journal= {arXiv preprint arXiv:2005.12711},
year = {2020}
}