Linear differential operators with distribution coefficients of various singularity orders

Abstract

In this paper, the linear differential expression of order $n\ge 2$ with distribution coefficients of various singularity orders is considered. We obtain the associated matrix for the regularization of this expression. Furthermore, we present the new statements of inverse spectral problems that consist in the recovery of differential operators with distribution coefficients from the Weyl matrix on the half-line and on a finite interval. The uniqueness theorems for these inverse problems are proved by developing the method of spectral mappings.

References in corpus (8)

• Inverse spectral problems for Sturm-Liouville operators with singular potentials
• Schrödinger operators with distributional potentials and boundary conditions dependent on the eigenvalue parameter
• Inverse spectral problems for energy-dependent Sturm-Liouville equations
• Supersymmetry and Schrödinger-type operators with distributional matrix-valued potentials
• Inverse spectral problems for Sturm--Liouville operators with matrix-valued potentials
• Reconstruction of higher-order differential operators by their spectral data
• Resonances for Euler-Bernoulli operator on the half-line
• Inverse scattering on the half-line for energy-dependent Schrödinger equations

Cited by in corpus (1)

• Reconstruction of higher-order differential operators by their spectral data