2023/04/12 by Ai-Wei Guan, Guan, Aiwei, Chuan‐Fu Yang +3 · 1 citation
Computer Science · Mathematics · #FOS: Mathematics #Matrix Theory and Algorithms #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2304.05747
openalex publication_date 2023/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we consider Barcilon's inverse problem, which consists of the recovery of the fourth-order differential operator from three spectra. We obtain the relationship of Barcilon's three spectra with the Weyl-Yurko matrix. Moreover, we prove the uniqueness theorem for the inverse problem solution by developing the ideas of the method of spectral mappings. Our approach allows us to obtain the result for the general case of complex-valued distributional coefficients. In the future, the methods and the results of this paper can be generalized to differential operators of orders greater than 4 and used for further development of the inverse problem theory for higher-order differential operators.