de Branges--Rovnyak spaces and Schur functions: The hyperholomorphic case

DOI10.1016/j.crma.2004.01.013zbMath1063.46019OpenAlexW1982772940MaRDI QIDQ1433381

Dan Volok, Michael V. Shapiro, Daniel Alpay

Publication date: 15 June 2004

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2004.01.013

Mathematics Subject Classification ID

Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Operator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc. (47A48)

Related Items

Quaternionic Hilbert spaces and a von Neumann inequality ⋮ de Branges–Rovnyak Spaces: Basics and Theory ⋮ Schur Analysis in the Quaternionic Setting: The Fueter Regular and the Slice Regular Case ⋮ Gleason's problem, rational functions and spaces of left-regular functions: the split-quaternion setting ⋮ Pontryagin-de Branges-Rovnyak spaces of slice hyperholomorphic functions ⋮ Schur functions and their realizations in the slice hyperholomorphic setting ⋮ Krein-Langer factorization and related topics in the slice hyperholomorphic setting ⋮ Rational functions associated with the white noise space and related topics ⋮ Point evaluation and Hardy space: the multiscale case ⋮ On discrete analytic functions: products, rational functions and reproducing kernels ⋮ On a polyanalytic approach to noncommutative de Branges-Rovnyak spaces and Schur analysis ⋮ Hyperholomorphic rational functions: the Clifford analysis case ⋮ Realization theorems for stationary multiscale systems

Cites Work

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• Rational functions and realization theory: The hyperholomorphic case
• A Beurling-Lax type theorem in the unit ball
• The curvature invariant of a Hilbert module over ℂ [z1, ..., zd]