Functional models of operators and their multivalued extensions in Hilbert space

DOI10.1007/s00020-020-02595-4zbMath1501.47022OpenAlexW3047733011MaRDI QIDQ2196525

Harry Dym, Damir Z. Arov

Publication date: 2 September 2020

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00020-020-02595-4

zbMATH Keywords

reproducing kernel Hilbert spacesmultiplication operatorslinear relationsfunctional modelsextensions of operators in Hilbert spacevector-valued de Branges spaces

Mathematics Subject Classification ID

Linear symmetric and selfadjoint operators (unbounded) (47B25) Dilations, extensions, compressions of linear operators (47A20) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Linear relations (multivalued linear operators) (47A06) Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) (47B32)

Related Items (2)

Vector valued de Branges spaces of entire functions based on pairs of Fredholm operator valued functions and functional model ⋮ Functional models for entire symmetric operators in rigged de Branges Pontryagin spaces

Cites Work

• Operational calculus of linear relations
• Self-adjoint extensions of symmetric subspaces
• On generalized resolvents and \(Q\)-functions of symmetric linear relations (subspaces) in Hilbert space
• M. G. Krein's lectures on entire operators
• Multivariate prediction, de Branges spaces, and related extension and inverse problems
• Multiplication operators with deficiency indices \((p,p)\) and sampling formulas in reproducing kernel Hilbert spaces of entire vector valued functions
• Defect subspaces and generalized resolvents of an Hermitian operator in the space \(\Pi_\kappa\)
• Resolvent matrix of Hermitian operator and the characteristic functions related to it
• Sous-espaces d'espaces vectoriels topologiques et noyaux associés. (Noyaux reproduisants.)
• On the spectral resolution of linear non-selfadjoint operators
• Multi-valued Operators/Linear Relations Between Kreĭn Spaces
• Boundary Value Problems, Weyl Functions, and Differential Operators
• Fundamental aspects of the representation theory of Hermitian operators with deficiency index (𝑚,𝑚)
• Preface
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