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

Fuente: arXiv
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Main Authors: Guan, Ai-Wei, Wu, Dong-Jie, Yang, Chuan-Fu, Bondarenko, Natalia P.
Format: Preprint
Published: 2025
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_version_ 1866910959881158656
author Guan, Ai-Wei
Wu, Dong-Jie
Yang, Chuan-Fu
Bondarenko, Natalia P.
author_facet Guan, Ai-Wei
Wu, Dong-Jie
Yang, Chuan-Fu
Bondarenko, Natalia P.
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2505_15675
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Borg-type theorem for a class of higher-order differential operators
Guan, Ai-Wei
Wu, Dong-Jie
Yang, Chuan-Fu
Bondarenko, Natalia P.
Spectral Theory
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.
title Borg-type theorem for a class of higher-order differential operators
topic Spectral Theory
url https://arxiv.org/abs/2505.15675