Para-orthogonal polynomials in frequency analysis

DOI10.1216/RMJM/1181069970zbMath1042.94001OpenAlexW2015934816MaRDI QIDQ1425670

Olav Njåstad, Leyla Daruis, Walter Van Assche

Publication date: 17 March 2004

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1216/rmjm/1181069970

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) Signal theory (characterization, reconstruction, filtering, etc.) (94A12) Application of orthogonal and other special functions (94A11)

Related Items (10)

Survey article: continued fractions associated with Wiener-Levinson filters, frequency analysis, moment theory and polynomials orthogonal on the unit circle ⋮ \(R_{II}\) type recurrence, generalized eigenvalue problem and orthogonal polynomials on the unit circle ⋮ Para-orthogonal polynomials on the unit circle satisfying three term recurrence formulas ⋮ Real orthogonal polynomials in frequency analysis ⋮ On the location of zeros of quasi-orthogonal polynomials with applications to some real self-reciprocal polynomials ⋮ Extreme zeros in a sequence of para-orthogonal polynomials and bounds for the support of the measure ⋮ Zeros of a family of hypergeometric para‐orthogonal polynomials on the unit circle ⋮ Orthogonal polynomials with respect to a family of Sobolev inner products on the unit circle ⋮ Extended relativistic Toda lattice, L-orthogonal polynomials and associated Lax pair ⋮ Zeros of para-orthogonal polynomials and linear spectral transformations on the unit circle

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The QR algorithm for unitary Hessenberg matrices
• Asymptotics for zeros of Szegő polynomials associated with trigonometric polynomial signals
• Generalized Szegö theory in frequency analysis
• Continued fractions and Szegö polynomials in frequency analysis and related topics
• Szegő polynomials and quadrature formulas on the unit circle
• Positive definite Toeplitz matrices, the Arnoldi process for isometric operators, and Gaussian quadrature on the unit circle
• Szegő polynomials applied to frequency analysis
• Some results about numerical quadrature on the unit circle
• Asymptotics of columns in the table of orthogonal polynomials with varying measures
• Orthogonal matrix polynomials and applications
• Gaussian quadrature for matrix valued functions on the unit circle
• Szegö polynomials associated with Wiener-Levinson filters
• Szegö quadrature formulas for certain Jacobi-type weight functions
• Moment Theory, Orthogonal Polynomials, Quadrature, and Continued Fractions Associated with the unit Circle

This page was built for publication: Para-orthogonal polynomials in frequency analysis