Infinite analogues of block Toeplitz matrices and related orthogonal functions

DOI10.1007/BF01203383zbMath0831.47017OpenAlexW2033306563MaRDI QIDQ1898014

David C. Lay, Robert L. Ellis, Israel Gohberg

Publication date: 20 September 1995

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

Full work available at URL: https://doi.org/10.1007/bf01203383

zbMATH Keywords

Hilbert modulematrix-valued functionsinfinite block matricesfinite block-Toeplitz matricesorthogonal for a matrix-valued inner product

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Eigenvalues, singular values, and eigenvectors (15A18) 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) Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX) (46H25)

Related Items (11)

The discrete twofold Ellis-Gohberg inverse problem ⋮ On a class of block Toeplitz matrices ⋮ On a class of extremal solutions of a moment problem for rational matrix-valued functions in the nondegenerate case. II ⋮ The Ellis-Gohberg inverse problem for matrix-valued Wiener functions on the line ⋮ The Twofold Ellis-Gohberg Inverse Problem for Rational Matrix Functions on the Real Line ⋮ The inverse problem for Ellis-Gohberg orthogonal matrix functions ⋮ A Connection between Szegö and Nehari Sequences in the Matrix-valued Case ⋮ Inversion formulas for infinite generalized Toeplitz matrices ⋮ Connections between the Carathéodory-Toeplitz and the Nehari extension problems: The discrete scalar case ⋮ On Canonical Solutions of a Moment Problem for Rational Matrix-valued Functions ⋮ Inverting Structured Operators Related to Toeplitz Plus Hankel Operators

Cites Work

• The prediction theory of multivariate stochastic processes. I. The regularity condition. - II. The linear predictor
• Orthogonal systems related to infinite Hankel matrices
• Orthogonal matrix-valued polynomials and applications. Seminar on operator theory at the School of Mathematical Sciences, Tel Aviv University (1987-1988)
• The square-integrability of matrix-valued functions with respect to a non-negative Hermitian measure
• Orthogonal polynomial matrices on the unit circle
• Inner Product Modules Over B ∗ -Algebras
• Modules Over Operator Algebras
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