Dirichlet Theorem for Jacobi-Dunkl Expansions

DOI10.1080/01630563.2020.1870042zbMath1465.33008OpenAlexW2950013558MaRDI QIDQ4985177

Iness Haouala, Frej Chouchene

Publication date: 22 April 2021

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/01630563.2020.1870042

zbMATH Keywords

quadratic mean convergenceJacobi-Dunkl polynomialsJacobi-Dunkl seriesDirichlet type theoremJacobi-Dunkl coefficients

Mathematics Subject Classification ID

Trigonometric approximation (42A10) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Convergence and divergence of series and sequences of functions (40A30) Other special orthogonal polynomials and functions (33C47) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16) Exponential and trigonometric functions (33B10)

Related Items (6)

Generalized distributions and Jacobi-Dunkl approximations ⋮ de La Vallée Poussin approximations and Jacobi-Dunkl convolution structures ⋮ On the approximation of functions by Jacobi-Dunkl expansions in the weighted space \({\mathbb{L}}_2^{\left(\alpha ,\beta \right)} \) ⋮ Harmonic analysis associated with the Jacobi-Dunkl operator on \((-\pi, \pi)\): exotic cases ⋮ Some direct and inverse theorems of approximation of functions in Jacobi-Dunkl discrete harmonic analysis ⋮ Fractional Jacobi-Dunkl transform: properties and application

Cites Work

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• Cesàro means of Jacobi expansions on the parabolic biangle
• Mean convergence of generalized Jacobi series and interpolating polynomials. II
• Summability of product Jacobi expansions
• Harmonic analysis associated with the Jacobi-Dunkl operator on \(-\frac{\pi}{2},\frac{\pi}{2}[\)]
• Mean convergence of generalized Jacobi series and interpolating polynomials. I
• Uniform convergence of Fourier--Jacobi series.
• Positivity and the convolution structure for Jacobi series
• Wiener type theorems for Jacobi series with nonnegative coefficients
• Approximation processes for fourier-jacobi expansions^†

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