Spectral analysis of non-local Schrödinger operators.

We study spectral properties of convolution operators L and their perturbations H = L + v ( x ) by compactly supported potentials. Results are applied to determine the front propagation of a population density governed by operator H with a compactly supported initial density provided that H has positive eigenvalues. If there is no positive spectrum, then the stabilization of the population density is proved. [ABSTRACT FROM AUTHOR]