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Extension unitaire et fonctions de représentation d’une contraction de classe \(C_ 1\) (Unitary extension and representating functions of a contraction of class \(C_ 1.)\). (French) Zbl 0583.47015

The authors study properties of a contraction operator T on a Hilbert space which is in the class \(C_ 1\). in the sense of Sz.-Nagy and Foias. They obtain an explicit limit expression for the Fourier coefficients of the scalar spectral measure for the *-residual part of the minimal unitary dilation of T. Various refinements of the Szegö infimum theorem and of the functional calculus of T are developed in this setting.
Reviewer: J.A.Ball

MSC:

47A45 Canonical models for contractions and nonselfadjoint linear operators
47A60 Functional calculus for linear operators
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