Completeness of the system of Floquet solutions of equations of the neutral type

The necessary and sufficient conditions for the completeness of the system of Floquet solutions, the eigenfunctions and associated functions of the displacement operator, over a period of the coefficient in metrics $C_1$ and $C$ in the space of all solutions of the equation $\dot y(t)=q(t)y(t-n\omega)+a\dot y(t-m\omega)$, are obtained. Here $q(t)$ is a continuous function of the period $\omega$.