Borg-type theorem for a class of higher-order differential operators

Ai-Wei Guan; Dong-Jie Wu; Chuan-Fu Yang; Natalia P. Bondarenko

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arXiv · 2505.15675

Borg-type theorem for a class of higher-order differential operators

Ai-Wei Guan·Dong-Jie Wu·Chuan-Fu Yang·Natalia P. Bondarenko

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Abstract

In this paper, we study an inverse spectral operator for the higher-order differential equation $(-1)^my^{(2m)}+ q y = \lambda y$, where $q \in L^2(0,\pi)$. 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.

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BibTeX RIS

Ai-Wei Guan, Dong-Jie Wu, Chuan-Fu Yang, Natalia P. Bondarenko. 2025-05-21. Borg-type theorem for a class of higher-order differential operators. https://arxiv.org/abs/2505.15675

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