Applied Physics and Mathematics Annotation << Back INVESTIGATION OF THE RESOLVENTS OF HIGHER-ORDER OPERATOR-DIFFERENTIAL EQUATIONS GIVEN ON THE SEGMENT N.S. BAYRAMOVA In this paper, we consider an operator given by a differential equation with given boundary conditions. It is proved that if the coefficients of the operator L satisfy the conditions (1)–(4), then the resolvent of the operator constructed using the boundary conditions (2) is an integral operator of the Hilbert-Schmidt type. Keywords: Hilbert space, resolvent, Hilbert-Schmidt integral operator, orthonormal vector functions, discrete spectrum. DOI: 10.25791/pfim.05.2022.1242 Pp. 31-35.