Resolvent formulas of general type and its application to point interactions

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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Received June 21, 2001; accepted September 4, 2001.

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Kuroda, S., Nagatani, H. Resolvent formulas of general type and its application to point interactions. J.evol.equ. 1, 421–440 (2001). https://doi.org/10.1007/PL00001381

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  • Key words: Resolvent formula, singular interaction, point interaction.