A general Christoffel-Darboux type formula

DOI10.1007/s00020-010-1776-9zbMath1217.65080OpenAlexW2051782882MaRDI QIDQ989600

Hugo J. Woerdeman

Publication date: 23 August 2010

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

Full work available at URL: https://doi.org/10.1007/s00020-010-1776-9

zbMATH Keywords

Schur complementChristoffel-Darboux formulamultivariate Toeplitz matricesoperator valued polynomial

Mathematics Subject Classification ID

Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56)

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Cites Work

• Unnamed Item
• Unnamed Item
• Classes of tuples of commuting contractions satisfying the multivariable von Neumann inequality
• Nest algebras and similarity transformations
• Unitary colligations, reproducing kernel Hilbert spaces, and Nevanlinna-Pick interpolation in several variables
• Factorization along commutative subspace lattices
• Scattering systems with several evolutions and multidimensional input/state/output systems
• Positive extension, Fejér-Riesz factorization and autoregressive filters in two variables
• The extension problem for positive-definite functions
• Bernstein-Szeg\"o measures on the two dimensional torus
• Estimates of inverses of multivariable Toeplitz matrices
• Inverses of Toeplitz Operators, Innovations, and Orthogonal Polynomials
• Nevanlinna-Pick interpolation on the bidisk
• Ando's theorem and sums of squares
• Outer factorizations in one and several variables