Schur functions and their realizations in the slice hyperholomorphic setting

DOI10.1007/s00020-011-1935-7zbMath1258.47018arXiv1110.2634OpenAlexW2067663024MaRDI QIDQ421113

Irene Sabadini, Fabrizio Colombo, Daniel Alpay

Publication date: 23 May 2012

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

Full work available at URL: https://arxiv.org/abs/1110.2634

zbMATH Keywords

Schur functionsreproducing kernelsrealizationsslice hyperholomorphic functionsS-resolvent operators

Mathematics Subject Classification ID

Functions of hypercomplex variables and generalized variables (30G35) Operator-theoretic methods (93B28) 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 (42)

Composition operators in Bloch spaces of slice hyperholomorphic functions ⋮ Slice Lebesgue measure of quaternions ⋮ The spectral theorem for unitary operators based on the \(S\)-spectrum ⋮ de Branges–Rovnyak Spaces: Basics and Theory ⋮ Schur Analysis in the Quaternionic Setting: The Fueter Regular and the Slice Regular Case ⋮ Slice Hyperholomorphic Functional Calculi ⋮ On power series expansions of the \(S\)-resolvent operator and the Taylor formula ⋮ Interpolation problems for certain classes of slice hyperholomorphic functions ⋮ Univalence results for slice regular functions of a quaternion variable ⋮ On some geometric properties of slice regular functions of a quaternion variable ⋮ On some notions of convergence for n -tuples of operators ⋮ On dual transform of fractional Hankel transform ⋮ Positivity, rational Schur functions, Blaschke factors, and other related results in the Grassmann algebra ⋮ Pontryagin-de Branges-Rovnyak spaces of slice hyperholomorphic functions ⋮ The Fueter-Sce mapping and the Clifford–Appell polynomials ⋮ Fractional powers of quaternionic operators and Kato’s formula using slice hyperholomorphicity ⋮ Functions of the infinitesimal generator of a strongly continuous quaternionic group ⋮ On pseudo-spectral factorization over the complex numbers and quaternions ⋮ Finite Blaschke products over quaternions: unitary realizations and zero structure ⋮ Krein-Langer factorization and related topics in the slice hyperholomorphic setting ⋮ The \(F\)-functional calculus for unbounded operators ⋮ Pick matricies and quaternionic power series ⋮ A new resolvent equation for the \(S\)-functional calculus ⋮ Invariant metrics for the quaternionic Hardy space ⋮ A new approach to slice analysis via slice topology ⋮ Slice regular Malmquist-Takenaka system in the quaternionic Hardy spaces ⋮ Bloch, Besov and Dirichlet spaces of slice hyperholomorphic functions ⋮ Beurling-Lax type theorems in the complex and quaternionic setting ⋮ The slice hyperholomorphic Bergman space on \(\mathbb {B}_{R}\): integral representation and asymptotic behavior ⋮ The spectral theorem for quaternionic unbounded normal operators based on the S-spectrum ⋮ Gleason's problem and Schur multipliers in the multivariable quaternionic setting ⋮ Distributions and the global operator of slice monogenic functions ⋮ Krein reproducing kernel modules in Clifford analysis ⋮ Essential S-spectrum for quaternionic quasi-compact operators on right quaternionic Hilbert spaces ⋮ Julia theory for slice regular functions ⋮ Realizations of holomorphic and slice hyperholomorphic functions: the Krein space case ⋮ Schatten class and Berezin transform of quaternionic linear operators ⋮ Perturbation of the generator of a quaternionic evolution operator ⋮ Quaternionic Fock space on slice hyperholomorphic functions ⋮ Boundary interpolation for slice hyperholomorphic Schur functions ⋮ Demicompactness results and Frobenuis Schur's decomposition for block operator matrices in right quaternionic Hilbert spaces ⋮ Realizations of slice hyperholomorphic generalized contractive and positive functions

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