Abstract
We develop scattering theory for non-local Schrödinger operators defined by functions of the Laplacian that include its fractional power (−Δ)ρ with \(0<\rho \leqslant 1\). 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.
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