Recovering differential operators with two constant delays under Dirichlet/Neumann boundary conditions.

This paper deals with non-self-adjoint differential operators with two constant delays generated by - y ′′ + q 1 ⁢ (x) ⁢ y ⁢ (x - τ 1) + (- 1) i ⁢ q 2 ⁢ (x) ⁢ y ⁢ (x - τ 2) {-y^{\prime\prime}+q_{1}(x)y(x-\tau_{1})+(-1)^{i}q_{2}(x)y(x-\tau_{2})} , where π 3 ≤ τ 2 < π 2 < 2 ⁢ τ 2 ≤ τ 1 < π {\frac{\pi}{3}\leq\tau_{2}<\frac{\pi}{2}<2\tau_{2}\leq\tau_{1}<\pi} and potentials q j {q_{j}} are real-valued functions, q j ∈ L 2 ⁢ [ 0 , π ] {q_{j}\in L^{2}[0,\pi]}. We will prove that the delays and the potentials are uniquely determined from the spectra of four boundary value problems: two of them under boundary conditions y ⁢ (0) = y ⁢ (π) = 0 {y(0)=y(\pi)=0} and the remaining two under boundary conditions y ⁢ (0) = y ′ ⁢ (π) = 0 {y(0)=y^{\prime}(\pi)=0}. [ABSTRACT FROM AUTHOR]