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Time cones and a functional model on a Riemann surface. (English. Russian original) Zbl 0738.47009
Math. USSR, Sb. 70, No. 2, 399-429 (1991); translation from Mat. Sb. 181, No. 7, 965-994 (1990).
Summary: Functional and triangular models of commuting systems of bounded linear operators are constructed. A method is given to construct dilations of multiparameter contraction semigroups. The subsequent analysis of these dilations within the scope of the Lax-Phillips scattering scheme leads to functional models on Riemann surfaces.

47A45 Canonical models for contractions and nonselfadjoint linear operators
47A20 Dilations, extensions, compressions of linear operators
47A40 Scattering theory of linear operators
47A67 Representation theory of linear operators
47D06 One-parameter semigroups and linear evolution equations
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