Regular factorizations of a characteristic function and singular operator-functions (Q1814364)
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scientific article; zbMATH DE number 10698
| Language | Label | Description | Also known as |
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| English | Regular factorizations of a characteristic function and singular operator-functions |
scientific article; zbMATH DE number 10698 |
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Regular factorizations of a characteristic function and singular operator-functions (English)
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25 June 1992
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Regular factorizations of contractive characteristic functions are studied in the book of \textit{B. Sz.-Nagy} and \textit{C. Foiaş} [Harmonic analysis of operators on Hilbert space. Budapest: Akadémiai Kiadó (1970; Zbl 0201.45003), Chapter 7]. It is shown that they correspond to invariant subspaces for the associated operator. In the present article, necessary and sufficient conditions are given for a factorization of a \(J\)-contractive operator characteristic function to be regular. The author explains the difference between this case and the Nagy-Foias criterion.
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characteristic functions
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invariant subspaces
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factorization of a \(J\)-contractive operator characteristic function
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