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Erschienen in:
2007 | OriginalPaper | Buchkapitel
On Connection Between Factorizations of Weighted Schur Functions and Invariant Subspaces
verfasst von : Alexey Tikhonov
Erschienen in: Operator Theory, Analysis and Mathematical Physics
Verlag: Birkhäuser Basel
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We study operator-valued functions of weighted Schur classes over multiply-connected domains. There is a correspondence between functions of weighted Schur classes and so-called “conservative curved” systems introduced in the paper. In the unit disk case the fundamental relationship between invariant subspaces of the main operator of a conservative system and factorizations of the corresponding Schur class function (characteristic function) is well known. We extend this connection to weighted Schur classes. With this aim we develop new notions and constructions and make suitable changes in standard theory.