Third-Order Differential Operators with a Second-Order Distribution Coefficient
Abstract
In this paper, we study differential operators associated with the formal expression $y''' + s(σ' y)' + s σ' y' + κσ'' y$ with distribution coefficient $σ'' \in W_3^{-2}$, where $s$ and $κ$ are constants. The uniqueness theorems are proved for the inverse spectral problems that consist in the recovery of $σ$ from the Weyl-Yurko matrix on a finite interval and on the half-line. In addition, we discuss the reconstruction of $σ$ and formulate some open problems.
Fields of Study & Subjects
Spectral Theory in Mathematical Physics
Mathematical Analysis and Transform Methods
Holomorphic and Operator Theory
Publication details
- Journal / source
- Mathematical Notes
- Publisher
- Pleiades Publishing Ltd
- Volume
- 119
- Issue
- 3-4
- Pages
- 535–540
- Publication date
- 1 April 2026
- Language
- EN