Mixed series of Jacobi and Chebyshev polynomials and their discretization

DOI10.1134/S0001434610070114zbMath1263.41017OpenAlexW2011448850MaRDI QIDQ650260

I. I. Sharapudinov, T. I. Sharapudinov

Publication date: 25 November 2011

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0001434610070114

zbMATH Keywords

analytic functionweighted Sobolev spaceChebyshev polynomialJacobi polynomialLebesgue inequalityultraspherical polynomialFourier-Jacobi series

Mathematics Subject Classification ID

Best approximation, Chebyshev systems (41A50)

Related Items (11)

Approximation properties of Fourier series of Sobolev orthogonal polynomials with Jacobi weight and discrete masses ⋮ Unnamed Item ⋮ Sobolev-orthogonal systems of functions associated with an orthogonal system ⋮ Polynomials orthogonal in the Sobolev sense, generated by Chebyshev polynomials orthogonal on a mesh ⋮ Sobolev orthogonal polynomials associated with Chebyshev polynomials of the first kind and the Cauchy problem for ordinary differential equations ⋮ Sobolev Orthogonal Polynomials Generated by Meixner Polynomials ⋮ Sobolev orthogonal polynomials generated by Jacobi and Legendre polynomials, and special series with the sticking property for their partial sums ⋮ Sobolev-orthogonal systems of functions and the Cauchy problem for ODEs ⋮ Sobolev-Orthonormal System of Functions Generated by the System of Laguerre Functions ⋮ Sobolev-orthogonal systems of functions and some of their applications ⋮ Fractal Sobolev systems of functions associated with orthonormal systems of functions

Cites Work

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• Approximationsfehler der Ableitungen von Interpolationspolynomen
• Approximation properties of the operators \({\mathcal Y}_{n+2r}(f)\) and of their discrete analogs
• A Rational Spectral Collocation Method with Adaptively Transformed Chebyshev Grid Points
• The basis property of the Legendre polynomials in the variable exponent Lebesgue space $ L^{p(x)}(-1,1)$
• Approximation of functions of variable smoothness by Fourier-Legendre sums
• Mixed series in ultraspherical polynomials and their approximation properties
• Mean Convergence of Jacobi Series

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