A general trace formula for the differential operator on a segment with the last coefficient perturbed by a finite signed measure

Spectral analysis of the Sturm-Liouville operator given on a system of segments

The spectral analysis of the Sturm-Liouville operator defined on a finite segment is the subject of an extensive literature. Sturm-Liouville operators on a finite segment are well studied and have numerous applications. The study of such operators already given on the system segments (graphs) was received in the works. This work is devoted to the study of operators $$(L_qy)(x)=col[-y_1''(x)+q_1(x)y_1(x), \ -y_2''(x)+q_2(x)y_2(x)],$$ where $y(x)=col[y_1(x),\ y_2(x)]εL^2(-a,0)\oplus L^2(0,b)=H, \ q_1(x), q_2(x) -$ real function $q_1εL^2(-a,0), q_2εL^2(0,b).$ Domain of definition $L_q$ has the fo…