Nagy–foiaş Type Functional Models of Nondissipative Operators in Parabolic Domains
نویسنده
چکیده
A functional model for nondissipative unbounded perturbations of an unbounded self-adjoint operator on a Hilbert space X is constructed. This model is analogous to the Nagy– Foias model of dissipative operators, but it is linearly similar and not unitarily equivalent to the operator. It is attached to a domain of parabolic type, instead of a half-plane. The transformation map from X to the model space and the analogue of the characteristic function are given explicitly. All usual consequences of the Nagy–Foias construction (the H∞ calculus, the commutant lifting, etc.) hold true in our context.
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Nagy–foiaş Type Functional Models of Nondissipative Operators in Non-convex Parabolic Domains
A functional model for nondissipative unbounded perturbations of an unbounded self-adjoint operator on a Hilbert space X is constructed. This model is analogous to the Nagy– Foias model of dissipative operators, but it is linearly similar and not unitarily equivalent to the operator. It is attached to a domain of parabolic type, instead of a half-plane. The transformation map from X to the mode...
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