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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.

MSC:
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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