2023/08/10 by Natalia P. Bondarenko, Bondarenko, Natalia P. · 1 citation
Computer Science · Mathematics · #34A55 34B09 34B40 34L05 46F10 #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.2308.05448
openalex publication_date 2023/08/10 · openalex created_date 2023/08/12 · openalex updated_date 2026/07/28
In this paper, we for the first time prove local solvability and stability of an inverse spectral problem for higher-order (n > 3) differential operators with distribution coefficients. The inverse problem consists in the recovery of differential equation coefficients from (n-1) spectra and the corresponding weight numbers. The proof method is constructive. It is based on the reduction of the nonlinear inverse problem to a linear equation in the Banach space of bounded infinite sequences. We prove that, under a small perturbation of the spectral data, the main equation remains uniquely solvable. Furthermore, we estimate the differences of the coefficients in the corresponding functional spaces.