Real orthogonal polynomials in frequency analysis

DOI10.1090/S0025-5718-04-01672-2zbMath1061.42013OpenAlexW1982316276MaRDI QIDQ4821052

Xin Li, A. Sri Ranga, Cleonice F. Bracciali

Publication date: 7 October 2004

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-04-01672-2

zbMATH Keywords

zerosSzegő polynomialsfrequency analysisquadraturespara-orthogonal polynomialsorthogonal polynomials on the real line

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Signal theory (characterization, reconstruction, filtering, etc.) (94A12) Application of orthogonal and other special functions (94A11)

Related Items (12)

\(R_{II}\) type recurrence, generalized eigenvalue problem and orthogonal polynomials on the unit circle ⋮ Para-orthogonal polynomials on the unit circle satisfying three term recurrence formulas ⋮ On the location of zeros of quasi-orthogonal polynomials with applications to some real self-reciprocal polynomials ⋮ Modified Chebyshev algorithm: some applications ⋮ Sobolev orthogonal polynomials on the unit circle and coherent pairs of measures of the second kind ⋮ Orthogonal polynomials on the unit circle and chain sequences ⋮ Zeros of a family of hypergeometric para‐orthogonal polynomials on the unit circle ⋮ Some properties of classes of real self-reciprocal polynomials ⋮ Positive trigonometric quadrature formulas and quadrature on the unit circle ⋮ Szegő type polynomials and para-orthogonal polynomials ⋮ A class of orthogonal functions given by a three term recurrence formula ⋮ Optimally Conditioned Vandermonde-Like Matrices

Uses Software

• Maple

Cites Work

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• Orthogonal polynomials - Constructive theory and applications
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• Para-orthogonal polynomials in frequency analysis
• Continued fractions and Szegö polynomials in frequency analysis and related topics
• Szegő polynomials applied to frequency analysis
• Szegö polynomials: Some relations to \(L\)-orthogonal and orthogonal polynomials
• An algorithm for Gaussian quadrature given modified moments
• Continuation methods for the computation of zeros of Szegő polynomials
• Szegö polynomials associated with Wiener-Levinson filters
• Moment Theory, Orthogonal Polynomials, Quadrature, and Continued Fractions Associated with the unit Circle
• A Strong Stieltjes Moment Problem
• A Refined Wiener–Levinson Method in Frequency Analysis
• Companion orthogonal polynomials: some applications

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