Method of Similar Operators in the Study of Spectral Properties of Perturbed First-Order Differential Operators.

In this paper, we consider first-order differential operators with periodic boundary conditions acting in a Hilbert space of square summable functions on the segment [0, ω] 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. [ABSTRACT FROM AUTHOR]