A special class of Jacobi series and some applications

DOI10.1016/0022-247X(72)90254-5zbMath0227.42007MaRDI QIDQ2549448

H. Bavinck

Publication date: 1972

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

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) General harmonic expansions, frames (42C15)

Related Items (18)

Jacobi translation and the inequality of different metrics for algebraic polynomials on an interval ⋮ Selective approximate identities for orthogonal polynomial sequences. ⋮ Gaussian random fields on the sphere and sphere cross line ⋮ On the saturation order of approximation processes involving Jacobi polynomials ⋮ Nikol'skii inequality between the uniform norm and \(L_q\)-norm with Jacobi weight of algebraic polynomials on an interval ⋮ Translation beyond Delsarte ⋮ Mean convergence of orthogonal series and Lagrange interpolation ⋮ Hardy spaces for Dunkl-Gegenbauer expansions ⋮ Approximation processes for fourier-jacobi expansions^† ⋮ The Hardy-Littlewood Theorem on Fractional Integration for Laguerre Series ⋮ Jacobi and Hankel multipliers of type \((p,q)\), \(1<p<q<\infty\) ⋮ On the integrability of Fourier-Jacobi transforms ⋮ Jacobi and Hankel multipliers of type \((p,q)\), \(1<p<q<\infty\) ⋮ On stable methods of summing Fourier-Laplace series ⋮ Central approximation processes ⋮ Characterizations of smoothness of functions in terms of the basis conjugate to Jacobi polynomials ⋮ Bohr-Favard inequality for functions on compact symmetric spaces of rank one ⋮ Jacobi weights, fractional integration, and sharp Ulyanov inequalities

Cites Work

• On the behavior of special classes of ultraspherical expansions. I, II
• Approximation theorems connected with generalized translations
• Integral representations for Jacobi polynomials and some applications
• A transplantation theorem for Jacobi series
• Convolution operators and L(p, q) spaces
• Modulus of continuity conditions for Jacobi series
• Positivity and the convolution structure for Jacobi series
• Special trigonometric series in 𝑘-dimensions
• A Convolution Structure for Jacobi Series
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