Krein-Langer factorization and related topics in the slice hyperholomorphic setting

DOI10.1007/s12220-012-9358-5zbMath1314.47036arXiv1204.5491OpenAlexW2089508833MaRDI QIDQ472037

Daniel Alpay, Irene Sabadini, Fabrizio Colombo

Publication date: 18 November 2014

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1204.5491

zbMATH Keywords

Schur functionsreproducing kernelsrealization\(S\)-resolvent operatorsslice~hyperholomorphic functions

Mathematics Subject Classification ID

Functions of hypercomplex variables and generalized variables (30G35) Operator theory over fields other than (mathbb{R}), (mathbb{C}) or the quaternions; non-Archimedean operator theory (47S10) Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) (47B32)

Related Items (19)

The spectral theorem for unitary operators based on the \(S\)-spectrum ⋮ 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 ⋮ On some notions of convergence for n -tuples of operators ⋮ Pontryagin-de Branges-Rovnyak spaces of slice hyperholomorphic functions ⋮ 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 ⋮ The \(F\)-functional calculus for unbounded operators ⋮ A new resolvent equation for the \(S\)-functional calculus ⋮ Beurling-Lax type theorems in the complex and quaternionic setting ⋮ 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 ⋮ Riesz projection and essential \(S\)-spectrum in quaternionic setting ⋮ Schatten class and Berezin transform of quaternionic linear operators ⋮ Boundary interpolation for slice hyperholomorphic Schur functions ⋮ Realizations of slice hyperholomorphic generalized contractive and positive functions

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