Abstract In this paper we consider a two–dimensional Hamiltonian integral system on an interval [ a, b) [ a, b). We investigate the definiteness and surjectivity properties and define associated with this system the maximal S S max and minimal S S min linear relations. For an improper gauge L L, we calculate the L L -resolvent matrix and describe the set of L L -resolvents of the linear relation S S min in the cases when the system is either quasiregular, limit circle, or limit point at b.
Derkach et al. (Sun,) studied this question.