@article{8b179c6afb4644859484089b098a72f5,
title = "Threshold Between Short and Long-range Potentials for Non-local Schr{\"o}dinger Operators",
abstract = "We develop scattering theory for non-local Schr{\"o}dinger operators defined by functions of the Laplacian that include its fractional power (−Δ)ρ with 0 < ρ⩽ 1. 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.",
keywords = "Bernstein function, Scattering theory, Wave operators",
author = "Atsuhide Ishida and Kazuyuki Wada",
note = "Funding Information: The first author was partially supported by the Grant-in-Aid for Young Scientists (B) #16K17633 and Scientific Research (C) #20K03625 from JSPS. Publisher Copyright: {\textcopyright} 2020, Springer Nature B.V.",
year = "2020",
month = sep,
day = "1",
doi = "10.1007/s11040-020-09356-0",
language = "English",
volume = "23",
journal = "Mathematical Physics Analysis and Geometry",
issn = "1385-0172",
publisher = "Springer Netherlands",
number = "3",
}