On indefinite abstract interpolation problem (Q2784971)
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scientific article; zbMATH DE number 1733189
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On indefinite abstract interpolation problem |
scientific article; zbMATH DE number 1733189 |
Statements
24 April 2002
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abstract interpolation
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unitary colligation
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Pontryagin space
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0.9086606
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On indefinite abstract interpolation problem (English)
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The abstract interpolation problem in the Schur class \(S\) was introduced by \textit{V. Eh. Katsnel'son, A. Ya. Khejfets} and \textit{P. M. Yuditskij} [Operators in functional spaces and questions of function theory, Collect. Sci. Works, Kiev, 83-96 (1987; Zbl 0703.41005)]. It contains the classical interpolation problems such as the moment problem, the Schur-Nevanlinna-Pick problem, and others. The author develops an indefinite version of the abstract interpolation problem. All its solutions are in the one-to-one correspondence with unitary extensions of an isometric operator on a model Pontryagin space included in a unitary colligation. The structure of the latter is studied.
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