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• W1562022668 abstract "For $S$ a contractive analytic operator-valued function on the unit disk ${mathbb D}$, de Branges and Rovnyak associate a Hilbert space of analytic functions ${mathcal H}(S)$ and related extension space ${mathcal D(S)}$ consisting of pairs of analytic functions on the unit disk ${mathbb D}$. This survey describes three equivalent formulations (the original geometric de Branges-Rovnyak definition, the Toeplitz operator characterization, and the characterization as a reproducing kernel Hilbert space) of the de Branges-Rovnyak space ${mathcal H}(S)$, as well as its role as the underlying Hilbert space for the modeling of completely non-isometric Hilbert-space contraction operators. Also examined is the extension of these ideas to handle the modeling of the more general class of completely nonunitary contraction operators, where the more general two-component de Branges-Rovnyak model space ${mathcal D}(S)$ and associated overlapping spaces play key roles. Connections with other function theory problems and applications are also discussed. More recent applications to a variety of subsequent applications are given in a companion survey article." @default.
• W1562022668 created "2016-06-24" @default.
• W1562022668 creator A5044821840 @default.
• W1562022668 creator A5081427672 @default.
• W1562022668 date "2015-01-01" @default.
• W1562022668 modified "2023-10-18" @default.
• W1562022668 title "de Branges–Rovnyak Spaces: Basics and Theory" @default.
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• W1562022668 doi "https://doi.org/10.1007/978-3-0348-0667-1_6" @default.
• W1562022668 hasPublicationYear "2015" @default.
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