Spectral Properties of the Cauchy Problem for a Second-Order Operator with Involution

We study the spectral properties of the Cauchy problem for the differential operator with an involution for satisfying the inequalities . Based on the analysis of the spectrum and the Green’s function constructed here, it is shown that if the parameter is irrational, then the system of root functions is complete but is not a basis in . In the opposite case, it is established that the root functions can be chosen to form an unconditional basis in .