An abstract interpolation problem and the extension theory of isometric operators

V E Katsnelson,P M Yuditskii,A Ya Kheifets

doi:10.1007/978-3-0348-8944-5_13

An abstract interpolation problem and the extension theory of isometric operators

V E Katsnelson, P M Yuditskii + Show 1 more

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https://doi.org/10.1007/978-3-0348-8944-5_13

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Publication Date: Jan 1, 1997

Citations: 34

#Extension Theory Of Operators #Abstract Interpolation Problem + Show 8 more

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Abstract

The algebraic structure of V.P. Potapov’s Fundamental Matrix Inequality (FMI) is discussed and its interpolation meaning is analyzed. Functional model spaces are involved. A general Abstract Interpolation Problem is formulated which seems to cover all the classical and recent problems in the field and the solution set of this problem is described using the Arov-Grossman formula. The extension theory of isometric operators is the proper language for treating interpolation problems of this type.

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