1999/11/25 by А. Г. Рамм, Ramm, A. G. · 1 citation
Computer Science · Engineering · Mathematics · #34B25 Secondary 81F05 #81F15 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical Analysis (math.NA) #Numerical methods in inverse problems #primary 35R30
paper · pdf · doi:10.48550/arxiv.math-ph/9911032
openalex publication_date 1999/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Property C stands for completeness of the set of products of solutions to homogeneous linear differential equations. property C is proved in various formulations for Schrödinger operators. Many applications of this property to inverse problems and inverse scattering problems are given. It is shown what part of the fixed-energy phase shifts determines a compactly supported potential uniquely. It is shown that the Newton-Sabatier method is not really an inversion method but a parameter-fitting procedure and it is proved that this procedure cannot recover a generic potential, in particular, any potential which is not analytic in a neighborhood of the positive real axis.