Spectral analysis of non-local Schrödinger operators

2016/03/04 by Yu. G. Kondratiev, Yu. Kondratiev, S. Molchanov +6
Mathematics · Physics and Astronomy · #47A10 #47D06 #60J85 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #advanced mathematical theories #math-ph #math.MP #math.SP #msc:47A10 #msc:47D06 #msc:60J85

paper · pdf · doi:10.48550/arxiv.1603.01626

openalex publication_date 2016/03/04 · arxiv created 2017/02/13 · arxiv updated 2017/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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