Zero-energy bound state decay for non-local Schrödinger operators

We consider solutions of the eigenvalue equation at zero energy for a class of non-local Schrödinger operators with potentials decreasing to zero at infinity. Using a path integral approach, we obtain detailed results on the spatial decay at infinity of both L2 and resonance solutions. We highlight the interplay of the kinetic term and the potential in these decay behaviours, and identify the decay mechanisms resulting from specific balances of global lifetimes with or without the potential.