2021/01/28 by Nabile Boussaïd, Boussaid, Nabile, Andrew Comech +1
Computer Science · Mathematics · #35P05 #47Axx #47B01 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2101.11979
openalex publication_date 2021/01/28 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
We develop a general approach to virtual levels in Banach spaces. We show\nthat virtual levels admit several characterizations which are essentially\nequivalent: (1) there are corresponding virtual states (from a certain larger\nspace); (2) there is no limiting absorption principle in their vicinity (e.g.\nno weights such that the ``sandwiched'' resolvent is uniformly bounded); (3) an\narbitrarily small perturbation can produce an eigenvalue.\n We provide applications to Schr "odinger operators with nonselfadjoint\nnonlocal potentials and in any dimension, deriving resolvent estimates in the\nneighborhood of the threshold when the corresponding operator has no virtual\nlevel there.\n