Comptes Rendus
Harmonic analysis
Equivalence of K-functionals and modulus of smoothness generated by a Dunkl type operator on the interval (-1,1)
Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1625-1633.

Our aim in this paper is to show that the modulus of smoothness and the K-functionals constructed from the Sobolev-type space corresponding to the Dunkl operator are equivalent on the interval (-1,1).

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Accepted:
Published online:
DOI: 10.5802/crmath.517
Classification : 43A30, 46E35, 33D60
Mots clés : Fourier–Dunkl series, Dunkl transform, generalized translation operator, $K$-functionals, modulus of smoothness

Faouaz Saadi 1; Radouan Daher 1

1 Department of Mathematics, Laboratory of Topology, Algebra, Geometry, and Discrete Mathematics, Faculty of Sciences Aïn Chock University Hassan II, Casablanca, Morocco
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Faouaz Saadi; Radouan Daher. Equivalence of K-functionals and modulus of smoothness generated by a Dunkl type operator on the interval $(-1, 1)$. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1625-1633. doi : 10.5802/crmath.517. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.517/

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