Approximation processes for fourier-jacobi expansions†

DOI10.1080/00036817608839133zbMath0341.41011OpenAlexW1981995747WikidataQ58166189 ScholiaQ58166189MaRDI QIDQ4108727

H. Bavinck

Publication date: 1976

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://ir.cwi.nl/pub/7729

Mathematics Subject Classification ID

Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) General harmonic expansions, frames (42C15) Approximation by polynomials (41A10) Special methods of summability (40G99) Saturation in approximation theory (41A40)

Related Items (17)

On the saturation order of approximation processes involving Jacobi polynomials ⋮ Complete asymptotic expansion for multivariate Bernstein-Durrmeyer operators and quasi-interpolants ⋮ Discrete Jacobi-Dunkl transform and approximation theorems ⋮ On the approximation of functions by Jacobi-Dunkl expansions in the weighted space \({\mathbb{L}}_2^{\left(\alpha ,\beta \right)} \) ⋮ Some direct and inverse theorems of approximation of functions in Jacobi-Dunkl discrete harmonic analysis ⋮ Generalized Lipschitz conditions for absolute convergence of weighted Jacobi-Dunkl series ⋮ Characterizations of smoothness of functions in terms of their Jacobi expansions ⋮ Hardy spaces for Dunkl-Gegenbauer expansions ⋮ Weighted approximation for the generalized discrete Fourier-Jacobi transform on space \(L_p(\mathbb{T})\) ⋮ REGULARIZED LEAST SQUARE REGRESSION WITH SPHERICAL POLYNOMIAL KERNELS ⋮ Saturation classes of the Cesàro and Abel-Poisson means of Fourier-Legendre series ⋮ Estimates for the modulus of continuity in the Jacobi frame ⋮ Approximation with Bernstein–Szegö polynomials ⋮ Dirichlet Theorem for Jacobi-Dunkl Expansions ⋮ Lipschitz spaces with respect to Jacobi translation ⋮ Characterizations of smoothness of functions in terms of the basis conjugate to Jacobi polynomials ⋮ Norm inequalities involving ordinary and Jacobi derivatives

Cites Work

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• Approximation theorems connected with generalized translations
• On the fundamental approximation theorems of D. Jackson, S.N. Bernstein and theorems of M. Zamansky and S.B. Stechkin
• Positivity and the convolution structure for Jacobi series
• Lipschitz spaces on compact manifolds
• A special class of Jacobi series and some applications
• Banach algebras for Jacobi series and positivity of a kernel
• The mean convergence of orthogonal series. III
• A Convolution Structure for Jacobi Series
• Limitierungsverfahren von Reihen mehrdimensionaler Kugelfunktionen und deren Saturationsverhalten

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