Special linear combinations of orthogonal polynomials

DOI10.1016/j.jmaa.2004.04.062zbMath1061.33008OpenAlexW2088220675MaRDI QIDQ1766712

Zinoviy Grinshpun

Publication date: 8 March 2005

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

Full work available at URL: https://doi.org/10.1016/j.jmaa.2004.04.062

zbMATH Keywords

Chebyshev polynomialsOrthogonal polynomialsWeight functionBernstein-Szegő polynomialsExtrema propertiesLinear combinationsLinearization coefficients

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 (13)

On a two-variable class of Bernstein-Szegő measures ⋮ On functions of the second kind in orthogonal polynomial theory ⋮ On the location of zeros of quasi-orthogonal polynomials with applications to some real self-reciprocal polynomials ⋮ Local perturbation of the discrete Schrödinger operator and a generalized Chebyshev oscillator ⋮ Orthogonality of quasi-orthogonal polynomials ⋮ On an inverse problem for a linear combination of orthogonal polynomials ⋮ Quadrature rules for polynomial modifications of Bernstein measures exact for analytic functions ⋮ Orthogonal polynomials associated with an inverse quadratic spectral transform ⋮ Characterizing the measures on the unit circle with exact quadrature formulas in the space of polynomials ⋮ Linear combinations of \(d\)-orthogonal polynomials ⋮ Zeros of linear combinations of Laguerre polynomials from different sequences ⋮ When do linear combinations of orthogonal polynomials yield new sequences of orthogonal polynomials? ⋮ Discriminants of classical quasi-orthogonal polynomials with application to Diophantine equations

Cites Work

• Mechanische Quadraturen mit positiven Cotesschen Zahlen
• On oscillatory properties of the Bernstein-Szegő orthogonal polynomials
• On Mechanical Quadratures, In Particular, with Positive Coefficients
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