Spectral analysis of non-local Schrödinger operators

Kondratiev Y, Molchanov S, Vainberg B. Spectral analysis of non-local Schrödinger operators. JOURNAL OF FUNCTIONAL ANALYSIS. 2017;273(3):1020-1048.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. (C) 2017 Elsevier Inc. All rights reserved