Exceptional points in Faddeev scattering problem

2014/07/06 by Evgeny Lakshtanov, Lakshtanov, Evgeny, B. Vaĭnberg +2
Computer Science · Mathematics · Physics and Astronomy · #34L25 #35P25 #47A40 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math-ph #math.MP #math.SP #msc:34L25 #msc:35P25 #msc:47A40

paper · pdf · doi:10.48550/arxiv.1407.1548

Minor corrections are made

openalex publication_date 2014/07/06 · arxiv created 2015/03/25 · arxiv updated 2020/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Exceptional points are values of the spectral parameter for which the homogeneous Faddeev scattering problem has a non-trivial solution. We study the existence/absence of exceptional points for small perturbations of conductive potentials of arbitrary shape and show that problems with absorbing potentials do not have exceptional points in a neighborhood of the origin. A criterion for existence of exceptional points is given.

Citations

• Global Uniqueness for a Two-Dimensional Inverse Boundary Value Problem

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