Multivariable Generalizations of the Schur Class: Positive Kernel Characterization and Transfer Function Realization

DOI10.1007/978-3-7643-8893-5_2zbMath1156.47018arXiv0705.2042OpenAlexW1554638391MaRDI QIDQ3612909

Joseph A. Ball, Quanlei Fang, Animikh Biswas, Sanne ter Horst

Publication date: 11 March 2009

Published in: Recent Advances in Operator Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0705.2042

zbMATH Keywords

Hilbert \(C^*\)-modulevon Neumann inequalitycontractive multipliercompletely positive definite kernelreproducing kernel Hilbert correspondence

Mathematics Subject Classification ID

Linear systems in control theory (93C05) Operator-theoretic methods (93B28) (C^*)-modules (46L08) Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56) Linear operator approximation theory (47A58) Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) (47B32) Crossed product algebras (analytic crossed products) (47L65)

Related Items (6)

Canonical Transfer-function Realization for Schur-Agler-class Functions of the Polydisk ⋮ Test functions, Schur-Agler classes and transfer-function realizations: the matrix-valued setting ⋮ Holomorphic functions on the symmetrized bidisk - realization, interpolation and extension ⋮ Progress in noncommutative function theory ⋮ On the Nevanlinna problem: characterization of all Schur–Agler class solutions affiliated with a given kernel ⋮ Noncommutative reproducing kernel Hilbert spaces

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