Kiselev and Simon ([13]) considered rank one singular perturbations of general type and formulate such perturbation in terms of a resolvent formula. In an attempt to generalize it beyond the rank one case, it is found that this expression in its generality describes resolvents of a rather wide class of closed operators (or all selfadjoint operators). Bounded operators from the domain of unperturbed operator with the graph norm to its dual space will serve as a parameter. As an application point interactions in one-dimension will be discussed systematically, recapturing selfadjoint boundary conditions associated to the problem.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.