Spectral analysis of non-local Schrödinger operators

Abstract

We study spectral properties of convolution operators $\mathcal{L}$ and their perturbations $H=\mathcal{L}+v(x)$ 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.

Cited by in corpus (2)

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• Stability and instability of steady states for a branching random walk