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Titlebook: Metric Constrained Interpolation, Commutant Lifting and Systems; C. Foias,A. E. Frazho,M. A. Kaashoek Book 1998 Springer Basel AG 1998 Ope

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Book 1998 the commutant lifting theorem from operator theory and the state space method from mathematical system theory. Initially the authors planned a number of papers treating nonstationary interpolation problems of Nevanlinna-Pick and Nehari type by reducing these nonstationary problems to stationary one
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Interpolation Problems for Operator-Valued Functionsnctions with operator arguments. Included are the Nevanlinna-Pick, Hermite-Fejér, Nehari, Sarason and Nudelman interpolation problems, in their classical and tangential form. Both one sided and two-sided versions are considered. Proofs of the main existence results will be given in the next chapter, based on the commutant lifting theorem.
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Nonstationary Interpolation Theoremsuantity which may be viewed as a discrete time parameter. In the next chapter time-varying systems will be used to give a motivation and a further interpretation of the role of this additional time parameter.
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Nonstationary Systems and Point Evaluation of point evaluation. It will also be shown how one may convert a time-varying system into an infinite dimensional time-invariant system, which gives a first insight into the reduction techniques that will be used later. Finally, a nonstationary version of the filtering problem is connected to a nonstationary Sarason problem.
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Central Commutant Liftingal properties of this central solution concern maximum entropy and mixed H. and L. bounds. Explicit formulas for the central intertwining lifting are given in different settings. As a first application an explicit solution of the operator-valued Schur problem is given.
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