Equivalence of K-functionals and modulus of smoothness generated by a Dunkl type operator on the interval $(-1, 1)$
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 $(-1,1)$.
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Académie des sciences
2023-11-01
|
| Series: | Comptes Rendus. Mathématique |
| Subjects: | |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.517/ |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1825206222031159296 |
|---|---|
| author | Saadi, Faouaz Daher, Radouan |
| author_facet | Saadi, Faouaz Daher, Radouan |
| author_sort | Saadi, Faouaz |
| collection | DOAJ |
| description | 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 $(-1,1)$. |
| format | Article |
| id | doaj-art-3a138104ce6a4b33b0bdeceaf3b095e8 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-11-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-3a138104ce6a4b33b0bdeceaf3b095e82025-02-07T11:11:47ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-11-01361G101625163310.5802/crmath.51710.5802/crmath.517Equivalence of K-functionals and modulus of smoothness generated by a Dunkl type operator on the interval $(-1, 1)$Saadi, Faouaz0Daher, Radouan1Department of Mathematics, Laboratory of Topology, Algebra, Geometry, and Discrete Mathematics, Faculty of Sciences Aïn Chock University Hassan II, Casablanca, MoroccoDepartment of Mathematics, Laboratory of Topology, Algebra, Geometry, and Discrete Mathematics, Faculty of Sciences Aïn Chock University Hassan II, Casablanca, MoroccoOur 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 $(-1,1)$.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.517/Fourier–Dunkl seriesDunkl transformgeneralized translation operator$K$-functionalsmodulus of smoothness |
| spellingShingle | Saadi, Faouaz Daher, Radouan Equivalence of K-functionals and modulus of smoothness generated by a Dunkl type operator on the interval $(-1, 1)$ Comptes Rendus. Mathématique Fourier–Dunkl series Dunkl transform generalized translation operator $K$-functionals modulus of smoothness |
| title | Equivalence of K-functionals and modulus of smoothness generated by a Dunkl type operator on the interval $(-1, 1)$ |
| title_full | Equivalence of K-functionals and modulus of smoothness generated by a Dunkl type operator on the interval $(-1, 1)$ |
| title_fullStr | Equivalence of K-functionals and modulus of smoothness generated by a Dunkl type operator on the interval $(-1, 1)$ |
| title_full_unstemmed | Equivalence of K-functionals and modulus of smoothness generated by a Dunkl type operator on the interval $(-1, 1)$ |
| title_short | Equivalence of K-functionals and modulus of smoothness generated by a Dunkl type operator on the interval $(-1, 1)$ |
| title_sort | equivalence of k functionals and modulus of smoothness generated by a dunkl type operator on the interval 1 1 |
| topic | Fourier–Dunkl series Dunkl transform generalized translation operator $K$-functionals modulus of smoothness |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.517/ |
| work_keys_str_mv | AT saadifaouaz equivalenceofkfunctionalsandmodulusofsmoothnessgeneratedbyadunkltypeoperatorontheinterval11 AT daherradouan equivalenceofkfunctionalsandmodulusofsmoothnessgeneratedbyadunkltypeoperatorontheinterval11 |