Linear differential operators with distribution coefficients of various singularity orders

Abstract

In this paper, the linear differential expression of order with distribution coefficients of various singularity orders is considered. We obtain the associated matrix for the regularization of this expression. Furthermore, we present new statements of inverse spectral problems that consist in the recovery of differential operators from the Weyl matrix on the half‐line and on a finite interval. The uniqueness theorems for these two inverse problems are proved by developing the method of spectral mappings. To the best of the author's knowledge, inverse problems for higher order differential operators with distribution coefficients on the half‐line have not been studied before. For the finite interval case, we for the first time consider the issue of recovering coefficients of the boundary conditions.