Direct and inverse problems for a third order self-adjoint differential operator with periodic boundary conditions and nonlocal potential

2022/12/20 by Yixuan Liu, Jun Yan, Liu, Yixuan +1
Mathematics · Computer Science · #Spectral Theory in Mathematical Physics #Numerical methods in inverse problems #Advanced Mathematical Modeling in Engineering

paper · pdf · doi:10.48550/arxiv.2212.10055

Abstract

A third order self-adjoint differential operator with periodic boundary conditions and an one-dimensional perturbation has been considered. For this operator, we first show that the spectrum consists of simple eigenvalues and finitely many eigenvalues of multiplicity two. Then the expressions of eigenfunctions and resolvent are described. Finally, the inverse problems for recovering all the components of the one-dimensional perturbation are solved. In particular, we prove the Ambarzumyan-type theorem and show that the even or odd potential can be reconstructed by three spectra.

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