2011/05/16 by Ognjen Milatovic, Milatovic, Ognjen · 1 citation
Computer Science · Mathematics · #35J10 #39A12 #47B25 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1105.3129
openalex publication_date 2011/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the context of a weighted graph with vertex set V and bounded vertex\ndegree, we give a sufficient condition for the essential self-adjointness of\nthe operator \Δ\σ+W, where \Δ\σ is the magnetic\nLaplacian and W colon V\→\ℝ is a function satisfying W(x)\≥\n-q(x) for all x\∈ V, with q colon V\→ [1,\∞). The condition is\nexpressed in terms of completeness of a metric that depends on q and the\nweights of the graph. The main result is a discrete analogue of the results of\nI. Oleinik and M. A. Shubin in the setting of non-compact Riemannian manifolds.\n