Method of similar operators in the study of spectral properties of perturbed first-order differential operators

In this paper, we considers first-order differential operators with periodic boundary conditions acting in a Hilbert space of square summable functions on the segment $[0,\omega] $ perturbed by Hilbert–Schmidt integral operators. A similarity transformation of the original operator to the operator of the block-diagonal structure is performed; this allows one to study spectral properties of the perturbed operator. The research method is the method of similar operators, which also presented in this work.