Equivalence of K-functionals and modulus of smoothness generated by a Dunkl type operator on the interval $(-1, 1)$

Faouaz Saadi; Radouan Daher

doi:10.5802/crmath.517

Analyse harmonique

Equivalence of K-functionals and modulus of smoothness generated by a Dunkl type operator on the interval

(- 1, 1)

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

Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1625-1633.

Résumé

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 $(- 1, 1)$ .

Reçu le : 2022-10-17
Révisé le : 2023-03-24
Accepté le : 2023-05-25
Publié le : 2023-11-17

DOI : 10.5802/crmath.517

Classification : 43A30, 46E35, 33D60
Mots clés : Fourier–Dunkl series, Dunkl transform, generalized translation operator, $K$-functionals, modulus of smoothness

Affiliations des auteurs :

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

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Faouaz Saadi and Radouan Daher},
     title = {Equivalence of {K-functionals} and modulus of smoothness generated by a {Dunkl} type operator on the interval $(-1, 1)$},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1625--1633},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {361},
     year = {2023},
     doi = {10.5802/crmath.517},
     language = {en},
}

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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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