Inverse Spectral Properties of the Quadratic Operator Pencil with Steplike Almost Periodic Potentials
Abstract
This paper investigates the inverse spectral properties of a quadratic operator pencil with steplike almost-periodic potentials in space $$L_{2}(R)$$ . The operator, which is generally non-self-adjoint, is analyzed under the conditions of specific potential forms. Key theorems are established to construct special solutions, examine spectral singularities, and demonstrate the absence of real eigenvalues. Additionally, the continuous spectrum is characterized, and the inverse spectral problem is formulated, providing a procedure to uniquely reconstruct the potentials from given spectral data. The findings contribute to the broader understanding of spectral theory in non-self-adjoint operator settings.
Fields of Study & Subjects
Spectral Theory in Mathematical Physics
Quantum Mechanics and Non-Hermitian Physics
Numerical methods in inverse problems
Publication details
- Journal / source
- Lobachevskii Journal of Mathematics
- Publisher
- Pleiades Publishing Ltd
- Volume
- 47
- Issue
- 2
- Pages
- 728–735
- Publication date
- 1 February 2026
- Language
- EN