Threshold Between Short and Long-range Potentials for Non-local Schrodinger Operators

Threshold Between Short and Long-range Potentials for Non-local Schrodinger Operators
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非本地薛定谔算子的短程势和远程势之间的阈值

DOI：
10.1007/s11040-020-09356-0
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发表时间：
2020
期刊：
Mathematical Physics, Analysis and Geometry
影响因子：
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通讯作者：
Atsuhide Ishida and Kazuyuki Wada
Atsuhide Ishida and Kazuyuki Wada
中科院分区：
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文献类型：
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作者：
Subaru Nomoto;Hiraku Nozawa;廣瀬　進;Atsuhide Ishida and Kazuyuki Wada

文献摘要

相似文献

我们发展了由拉普拉斯函数定义的非局部薛定谔算子的散射理论，该函数包含其分数次幂(−Δ)ρ与.特别地，我们的函数比Bernstein函数集属于更广泛的类。通过证明波算符的存在和不存在，我们阐明了微扰势的短程和长程衰变条件之间的阈值。
We develop scattering theory for non-local Schrödinger operators defined by functions of the Laplacian that include its fractional power (−Δ)ρwith. 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.