Geodesic
Hull-range potentials and M. G. Krein's formula for generalized resolvents
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XV, Tome 149 (1986), pp. 7-23 
V. M. Adamyan; B. S. Pavlov. Hull-range potentials and M. G. Krein's formula for generalized resolvents. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XV, Tome 149 (1986), pp. 7-23. http://geodesic.mathdoc.fr/item/ZNSL_1986_149_a0/
@article{ZNSL_1986_149_a0,
     author = {V. M. Adamyan and B. S. Pavlov},
     title = {Hull-range potentials and {M.~G.~Krein's} formula for generalized resolvents},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {7--23},
     year = {1986},
     volume = {149},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1986_149_a0/}
}
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For non-additive finite dimensional perturbations of an Hermitian operator Krein's formula is used to obtain arepresentation of scattering matrices with Hermitian $(n\times n)$-matrix as a parameter. Relying on this representation, we obtain explicit formulae for a number of new models of quantum mechanics with null-range potential. We also establish a connection of the parametrization obtained with phenomenological $S$-matrices and relevant Wigner's $R$-functions.