Year: 2025
Type: preprint
Abstract: In this paper, we study an inverse spectral operator for the higher-order differential equation $(-1)^my^{(2m)}+ q y = λy$, where $q \in L^2(0,π)$. We prove that if $\|q\|_2$ is sufficiently small, the two spectra corresponding to the both Dirichlet boundary conditions and to the Dirichlet-Neumann ones uniquely determine the potential $q$. The result extends the Borg theorem from the second order to all even higher orders.
Source: arXiv (Cornell University)
Authors: Guan, Ai-Wei, Wu, Dong-Jie, Yang, Chuan-Fu, Bondarenko, Natalia P.
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G4079248702
OpenAlex ID: W4415329255
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