Local Solvability and Stability of an Inverse Spectral Problem for Higher-Order Differential Operators

In this paper, we, for the first time, prove the local solvability and stability of an inverse spectral problem for higher-order ((Formula presented.)) differential operators with distribution coefficients. The inverse problem consists of the recovery of differential equation coefficients from (Formula presented.) 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. © 2023 by the author.