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Analysis of inverse spectral operator indicates potential determination from two spectra in boundary conditions.
In this paper, we study an inverse spectral operator for the higher-order differential equation (-1)ᵐy⁽²ᵐ⁾+ q y = λ y, where q ∈ L²(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.
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Guan et al. (2025) studied this question.
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