Defines resolvent matrices in Hamiltonian systems, revealing properties and implications in specific conditions.
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 Sₘₐₓ S max and minimal Sₘᵢₙ 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 Sₘᵢₙ S min in the cases when the system is either quasiregular, limit circle, or limit point at b .
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Derkach et al. (2026) studied this question.