CMV matrices, a matrix version of Baxter's theorem, scattering and de Branges spaces

DOI10.4171/EMSS/14zbMath1346.42032OpenAlexW2398252915MaRDI QIDQ726759

Harry Dym, David P. Kimsey

Publication date: 14 July 2016

Published in: EMS Surveys in Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/emss/14

zbMATH Keywords

reproducing kernel Hilbert spacesNehari problemscattering matricesmatrix orthogonal polynomialsde Branges spacesBaxter's theoremSchur parameters CMV matrices

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) Linear operator methods in interpolation, moment and extension problems (47A57) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Jacobi (tridiagonal) operators (matrices) and generalizations (47B36) Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) (47B32)

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Cites Work

• Scattering theory for CMV matrices: Uniqueness, Helson-Szegő and strong Szegő theorems
• Orthogonal polynomials and Padé approximants associated with a system of arcs
• Classes of linear operators. Vol. II
• Scattering theory and matrix orthogonal polynomials on the real line
• Szegő's theorem and its probabilistic descendants
• Multivariate prediction and matrix Szegő theory
• CMV matrices: Five years after
• Trace formulas for a class of truncated block Toeplitz operators
• Tutorial on a Nehari Problem and Related Reproducing Kernel Spaces
• Schur Parametrization of Positive Definite Block-Toeplitz Systems
• The Analytic Theory of Matrix Orthogonal Polynomials
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• Orthogonal polynomial matrices on the unit circle
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