On the spectrum of an odd-order differential operator (Q2401639)

Consider the boundary eigenvalue problem \[ \begin{gathered} i^{-n} y^{(n)}(x)=\lambda y(x)\quad\text{for }0\leq x\leq 1,\\ y(0)+ \alpha_0 y(1)= 0,\;y'(0)+ \alpha_1y'(1)=0,\dots, y^{(n-1)}(0)+ \alpha_n y^{(n-1)}(0)= 0.\end{gathered}\tag{\(*\)} \] The author proves that in the case of odd \(n\) the coefficients \(\alpha_i\) can be choosen in such a way that the spectrum of \((*)\) fills the whole complex plane.