SPECTRAL PROPERTIES OF AN IMPULSIVE STURM–LIOUVILLE OPERATOR WITH COMPLEX PERIODIC COEFFICIENTS

This study focuses on exploring the spectral properties and scattering function of the impulsive operator generated by the Sturm–Liouville equation with complex periodic potentials. We introduce a new approach to investigate the spectral singularities and eigenvalues of the operator. Additionally, we establish the finiteness of eigenvalues and spectral singularities with finite multiplicities under specific conditions.