Inverse problems for Dirac operators with a constant delay less than half of the interval

2023/05/18 by F. Y. Wang, Wang, Feng, Chuan‐Fu Yang +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2305.10752

openalex publication_date 2023/05/18 · openalex created_date 2023/05/21 · openalex updated_date 2026/07/28

Abstract

In this work, we consider Dirac-type operators with a constant delay less than half of the interval and not less than two-fifths of the interval. For our considered Dirac-type operators, two inverse spectral problems are studied. Specifically, reconstruction of two complex L₂-potentials is studied from complete spectra of two boundary value problems with one common Dirichlet boundary condition and Neumann boundary condition, respectively. We give answers to the full range of questions usually raised in the inverse spectral theory. That is, we give uniqueness, necessary and sufficient conditions of the solvability, reconstruction algorithm and uniform stability for our considered inverse problems.

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