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

In this paper, we study an inverse spectral operator for the higher-order differential equation $(-1{)}^m{y}^{(2m)}+qy=\lambda y$, where $q\in L^2(0,\pi )$. We prove that if $\mathrm{\parallel }q{\mathrm{\parallel }}_2$ 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.