Mathematics – Functional Analysis
Scientific paper
2009-12-10
Mathematics
Functional Analysis
46 pages
Scientific paper
In the PhD thesis of the second author under the supervision of the third author was defined the class SI of J-contractive functions, depending on a parameter and arising as transfer functions of overdetermined conservative $2D$ systems invariant in one direction. In this paper we extend and solve in the class SI, a number of problems originally set for the class SC of functions contractive in the open right-half plane, and unitary on the imaginary line with respect to some preassigned signature matrix J. The problems we consider include the Schur algorithm, the partial realization problem and the Nevanlinna-Pick interpolation problem. The arguments rely on a correspondence between elements in a given subclass of SI and elements in SC. Another important tool in the arguments is a new result pertaining to the classical tangential Schur algorithm.
Alpay Daniel
Melnikov Alexander
Vinnikov Victor
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