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* Partially supported by Grant MM-428/94 of MESC.In this paper we present some generalizations of results of M.
S. Livšic [4,6], concerning regular colligations (A1, A2, H, Φ, E, σ1, σ2, γ, ˜γ)
(σ1 > 0) of a pair of commuting nonselfadjoint operators A1, A2 with finite
dimensional imaginary parts, their complete characteristic functions and a
class Ω(σ1, σ2) of operator-functions W(x1, x2, z): E → E in the case of
an inner function W(1, 0, z) of the class Ω(σ1). ...
The characteristic function for a contraction is a classical complete unitary invariant devised by Sz.-Nagy and Foiaş. Just as a contraction is related to the Szegö kernel for |z|,|w| < 1, by means of , we consider an arbitrary open connected domain Ω in ℂⁿ, a complete Pick kernel k on Ω and a tuple T = (T₁, ..., Tₙ) of commuting bounded operators on a complex separable Hilbert space ℋ such that (1/k)(T,T*) ≥ 0. For a complete Pick kernel the 1/k functional calculus makes sense in a beautiful...
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