Resolvent formulas of general type and its application to point interactions

Journal of Evolution Equations (Impact Factor: 0.64). 11/2001; 1(4):421-440. DOI: 10.1007/PL00001381

ABSTRACT 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.

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