Nonstationary analogs of the Herglotz representation theorem: The discrete case

DOI10.1006/jfan.1999.3426zbMath0984.47008OpenAlexW1966664991MaRDI QIDQ1304654

Aalt Dijksma, Daniel Alpay, Yossi (Joseph) Peretz

Publication date: 5 May 2002

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://pure.rug.nl/ws/files/3149110/1999JFunctAnalAlpay.pdf

zbMATH Keywords

matrix-valued measurebilateral shiftoperator colligationsfractional-linear-transformation with matrix coefficientsHerglotz formulamatrix formula

Mathematics Subject Classification ID

Canonical models for contractions and nonselfadjoint linear operators (47A45) Quasitriangular and nonquasitriangular, quasidiagonal and nonquasidiagonal linear operators (47A66)

Related Items

Herglotz functions: the Fueter variables case, Linear stochastic systems: a white noise approach, Carathéodory functions in the Banach space setting

Cites Work

• Hilbert spaces of analytic functions, inverse scattering and operator models. I
• Perturbation theory
• Unitary colligations, reproducing kernel Hilbert spaces, and Nevanlinna-Pick interpolation in several variables
• On the Hankel-norm approximation of upper-triangular operators and matrices
• Bitangential interpolation for input-output maps of time-varying systems: The continuous time case
• Two-sided Nudelman interpolation for input-output operators of discrete time-varying systems
• Schur parameters, factorization and dilation problems
• Complementation in Krein Spaces
• Time-variant displacement structure and interpolation problems
• Interpolation problems, extensions of symmetric operators and reproducing kernel spaces. II
• Interpolation problems, extensions of symmetric operators and reproducing kernel spaces. II
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item