Necessary and Sufficient Conditions for the Solvability of Inverse Problem for a Class of Dirac Operators

2014/04/01 by Kh. R. Mamedov, Mamedov, Kh. R., Özge Akçay +1
Mathematics · #34A55 #34L40 #Differential Equations and Boundary Problems #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · doi:10.48550/arxiv.1404.0192

openalex publication_date 2014/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider a problem for the first order Dirac differential equations system with spectral parameter dependent in boundary condition. The asymptotic behaviors of eigenvalues, eigenfunctions and normalizing numbers of this system are investigated. The expansion formula with respect to eigenfunctions is obtained and Parseval equality is given. The main theorem on necessary and sufficient conditions for the solvabilty of inverse problem is proved and the algorithm of reconstruction of potential from spectral data (the sets of eigenvalues and normalizing numbers) is given.

Related

• Necessary and Sufficient Conditions for Solvability of Inverse Problem for Dirac Operators with Discontinuous Coefficient
• Inverse Problem for a Class of Dirac Operators with Spectral Parameter\n Contained in Boundary Conditions
• Recovery of the matrix potential of the one-dimensional Dirac equation from spectral data
• Inverse Problems For Dirac Operators With a Finite Number of Transmission Conditions
• Inverse problems for Dirac operators with a constant delay less than half of the interval