Abstract
Let w(λ) be an operator function, holomorphic in the domain Ω, with a reproducing kernel that is Hermitian positive with respect to the semiplane. Then w(λ) coincides with the characteristic function (c.f.) of a pencil λA+B of bounded operators, where the pencil is determined up to unitary equivalence. A connection between the invariants of the pencil and the divisors of its characteristic function is established. A universal model of an arbitrary pencil and a triangular model under the condition AB*+BA* ∈ σw are constructed.
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