Non-physical sheet for the Friedrichs model

The way of deducing expansion theorem by resonance states for two-dimensional Friedrichs model $A=\frac1{2i}(U_\varphi-U_\varphi^+)$ is suggested. The construction is based on detail Lax–Phillips analogues of corresponding unitary Friedrichs model $U_\varphi=z\left(1+\frac{2i\alpha}{1-i\alpha}P_\varphi\right)$ perturbed by projector $P_\varphi$, generated by an element $\varphi$, possesing special analytical properties.