Polynomial Schauder basis of optimal degree with Jacobi orthogonality

DOI10.1016/j.jat.2013.06.003zbMath1281.42027OpenAlexW1975749907MaRDI QIDQ390625

Jörn Schnieder, Jürgen Prestin

Publication date: 8 January 2014

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

Full work available at URL: https://doi.org/10.1016/j.jat.2013.06.003

zbMATH Keywords

hypergeometric functionsSchauder basisasymptotic approximationJacobi polynomialsBessel functionsapproximation by polynomials

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) Approximation by polynomials (41A10)

Cites Work

• Polynomial operators and local smoothness classes on the unit interval
• Local convergence of Fourier series with respect to periodized wavelets
• Orthogonal algebraic polynomial Schauder bases of optimal degree
• On polynomial bases for the space \(C[-1,1\)]
• A note on orthonormal polynomial bases and wavelets
• Growth of degrees of polynomial bases
• Orthogonal trigonometric Schauder bases of optimal degree for \(C(K)\)
• A uniform asymptotic expansion for Jacobi polynomials via uniform treatment of Darboux's method
• Localized polynomial frames on the interval with Jacobi weights
• On an orthonormal polynomial basis in the space C[-1,1]
• Orthogonal polynomial Schauder bases in $ C \lbrack -1,1 \rbrack $ with optimal growth of degrees
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