On characterization theorems for measures associated with orthogonal systems of rational functions on the unit circle

DOI10.1016/0021-9045(92)90060-2zbMath0763.42016OpenAlexW1968221143MaRDI QIDQ1198156

S. Singh

Publication date: 16 January 1993

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-9045(92)90060-2

zbMATH Keywords

orthogonal rational functions\(n\)th root asymptoticsreproducing kernelsSzegő classMalmquist systemorthogonal polynomials for measuresratio-asymptotics

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Completeness of sets of functions in nontrigonometric harmonic analysis (42C30)

Related Items

Generalized Szegö theory in frequency analysis ⋮ Orthogonal rational functions on the extended real line and analytic on the upper half plane ⋮ The convergence properties of orthogonal rational functions on the extended real line and analytic on the upper half plane ⋮ Asymptotic properties of zeros of orthogonal rational functions ⋮ Asymptotics for Orthogonal Rational Functions ⋮ Strong and weak convergence of orthogonal systems of rational functions on the unit circle ⋮ On orthogonal systems of rational functions on the unit circle and polynomials orthogonal with respect to varying measures ⋮ Moment problems and orthogonal functions

Cites Work

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• Behavior of best \(L_ p\) polynomial approximants on the unit interval and on the unit circle
• Asymptotics for the ratio of leading coefficients of orthonormal polynomials on the unit circle
• Orthogonal rational functions and tridiagonal matrices
• A class of orthogonal polynomials
• Positive multipoint Padé continued fractions
• On a generalized Szegö- Levinson realization algorithm for optimal linear predictors based on a network synthesis approach