Equivalence of \(K\)-functionals and modulus of smoothness generated by a generalized Jacobi-Dunkl transform on the real line

DOI10.1007/s12215-020-00520-7zbMath1483.44003OpenAlexW3089255198MaRDI QIDQ2047441

Radouan Daher, Othman Tyr

Publication date: 20 August 2021

Published in: Rendiconti del Circolo Matemàtico di Palermo. Serie II (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12215-020-00520-7

zbMATH Keywords

modulus of smoothness\(K\)-functionalsJacobi-Dunkl operatorJacobi-Dunkl Laplacian operatorJacobi-Dunkl translation

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Integral transforms of special functions (44A20) Rate of convergence, degree of approximation (41A25)

Related Items (5)

Jackson theorems for the quaternion linear canonical transform ⋮ Discrete Jacobi-Dunkl transform and approximation theorems ⋮ Modulus of smoothness and approximation theorems in Clifford analysis ⋮ Some direct and inverse theorems of approximation of functions in Jacobi-Dunkl discrete harmonic analysis ⋮ Integrability of the Fourier–Jacobi transform of functions satisfying Lipschitz and Dini–Lipschitz-type estimates

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• Fourier–Jacobi harmonic analysis and some problems of approximation of functions on the half-axis in L₂ metric: Jackson's type direct theorems
• Equivalence of K-functionals and modulus of smoothness constructed by generalized Jacobi transform

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