Geodesic
Operators close to unitary and their function models.~1
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 26, Tome 255 (1998), pp. 82-91

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We construct a function model for an operator in Hilbert space, which is close to an isometry. The model operator acts on a space of functions meromorphic inside and outside the unit disk. The functions from the space may be regarded as a generalization of Cauchy integrals of distributions, which gives a base for spectral analysis. The first part included in this issue contains a theorem on the existence of such a model for one-dimensional perturbations of a unitary operator. 
@article{ZNSL_1998_255_a4,
     author = {V. V. Kapustin},
     title = {Operators close to unitary and their function models.~1},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {82--91},
     publisher = {mathdoc},
     volume = {255},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1998_255_a4/}
}
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V. V. Kapustin. Operators close to unitary and their function models.~1. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 26, Tome 255 (1998), pp. 82-91. http://geodesic.mathdoc.fr/item/ZNSL_1998_255_a4/