de Branges–Rovnyak Spaces and Norm-Constrained Interpolation

Joseph A. Ball () and Vladimir Bolotnikov ()
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Joseph A. Ball: Virginia Tech, Department of Mathematics
Vladimir Bolotnikov: The College of William and Mary, Department of Mathematics

Chapter 28 in Operator Theory, 2015, pp 681-720 from Springer

Abstract: Abstract For S a contractive analytic operator-valued function on the unit disk 𝔻 $$\mathbb{D}$$ , de Branges and Rovnyak associate a Hilbert space of analytic functions ℋ ( S ) $$\mathcal{H}(S)$$ . A companion survey provides equivalent definitions and basic properties of these spaces as well as applications to function theory and operator theory. The present survey brings to the fore more recent applications to a variety of more elaborate function theory problems, including H ∞ -norm constrained interpolation, connections with the Potapov method of Fundamental Matrix Inequalities, parametrization for the set of all solutions of an interpolation problem, variants of the Abstract Interpolation Problem of Katsnelson, Kheifets, and Yuditskii, boundary behavior and boundary interpolation in de Branges–Rovnyak spaces themselves, and extensions to multivariable and Kreĭn-space settings.

Keywords: Fundamental Matrix Inequality; Abstract Interpolation Problem; Potapov's Method; Schur-class Function; Reproducing Kernel Hilbert Space (RKHS) (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-0667-1_5

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DOI: 10.1007/978-3-0348-0667-1_5

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