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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Funding
This research was supported by the Fundamental Research Funds for the Central Universities of Civil Aviation University of China (Grant No. 3122022061); National Natural Science Foundation of China (Grant No. 12001153).
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Liu, Y., Yan, J. Direct and Inverse Problems for a Third Order Self-Adjoint Differential Operator with Periodic Boundary Conditions and Nonlocal Potential. Results Math 79, 21 (2024). https://doi.org/10.1007/s00025-023-02052-9
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DOI: https://doi.org/10.1007/s00025-023-02052-9