Simple matrix representations of the orthogonal polynomials for a rational spectral density on the unit circle

DOI10.1016/j.jmaa.2018.04.062zbMath1390.33022OpenAlexW2801940259MaRDI QIDQ1754693

Yukio Kasahara, Akihiko Inoue

Publication date: 31 May 2018

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/2115/79065

zbMATH Keywords

orthogonal polynomials on the unit circleVerblunsky coefficientsrational spectral densitySeghier's formula

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05)

Related Items (2)

Representation theorems in finite prediction, with applications ⋮ Closed-form expression for finite predictor coefficients of multivariate ARMA processes

Cites Work

• An explicit representation of Verblunsky coefficients
• Time series: theory and methods.
• Prediction d'un processus stationnaire du second ordre de covariance connue sur un intervalle fini
• Partial autocorrelation functions of the fractional ARIMA processes with negative degree of differencing.
• Asymptotics for the partial autocorrelation function of a stationary process
• Asymptotic behavior for partial autocorrelation functions of fractional ARIMA processes.
• AR and MA representation of partial autocorrelation functions, with applications
• Explicit representation of finite predictor coefficients and its applications
• Some uniqueness theorems for \(H^p(U^n)\) functions
• Verblunsky coefficients and Nehari sequences
• Unnamed Item
• Unnamed Item

This page was built for publication: Simple matrix representations of the orthogonal polynomials for a rational spectral density on the unit circle