Operators close to unitary and their function models. 1

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.