2015/10/10 by Khanlar R. Mamedov, Mamedov, Khanlar R., Özge Akçay +1
Mathematics · #34A55 #34L40 #Differential Equations and Boundary Problems #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1510.02912
openalex publication_date 2015/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work, a complete solution of the inverse spectral problem for a class of Dirac differential equations system is given by spectral data (eigenvalues and normalizing numbers). As a direct problem, the eigenvalue problem is solved: the asymptotic formulas of eigenvalues, eigenfunctions and normalizing numbers of problem are obtained, spectral data is defined by the sets of eigenvalues and normalizing numbers. The expansion formula with respect to eigenfunctions is obtained. Gelfand-Levitan-Marchenko equation is derived. The main theorem on necessary and sufficient conditions for the solvability of inverse spectral problem is proved and the algorithm of reconstruction of potential from spectral data is given.