I am encountering non-local (nonlinear) PDEs in my work. To compute stability, I am trying to numerically estimate the spectrum of linearized-but-nonlocal version of the said PDEs.

However, I am not sure if all the lessons from the local PDE spectral theory apply here. So I am looking for a good reference/monograph/review paper which describes the subtle points in nonlocal spectral theory and/or stability analysis.