Equivalence ofK-functionals and modulus of smoothness generated by a generalized Jacobi-Dunkl transform on the real line

被引：5

作者：

Daher, Radouan ^{[1
]}

Tyr, Othman ^{[1
]}

机构：

[1] Univ Hassan 2, Fac Sci Ain Chock, Dept Math, Casablanca, Morocco

来源：

RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO | 2021年 / 70卷 / 02期

关键词：

Jacobi-Dunkl operator; Jacobi-Dunkl Laplacian operator; Jacobi-Dunkl translation; K-functionals; Modulus of smoothness; HARMONIC-ANALYSIS; OPERATOR;

D O I：

10.1007/s12215-020-00520-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Using the generalized Jacobi-Dunkl translation, we prove the equivalence between modulus of smoothness andK-functional constructed by the Sobolev space corresponding to the Jacobi-Dunkl Laplacian operator.

引用

页码：687 / 698

页数：12

共 19 条

[1] Equivalence of K-functionals and modulus of smoothness generated by a generalized Jacobi–Dunkl transform on the real line
Radouan Daher
Othman Tyr
Rendiconti del Circolo Matematico di Palermo Series 2, 2021, 70 : 687 - 698
[2] Equivalence of K-functionals and modulus of smoothness constructed by generalized Jacobi transform
El Hamma, Mohamed
Daher, Radouan
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2019, 30 (12) : 1018 - 1024
[3] Equivalence of K-Functionals and Modulus of Smoothness Constructed by Generalized Dunkl Translations
Belkina, E. S.
Platonov, S. S.
RUSSIAN MATHEMATICS, 2008, 52 (08) : 1 - 11
[4] Equivalence of K-functionals and modulus of smoothness constructed by generalized Dunkl translations
E. S. Belkina
S. S. Platonov
Russian Mathematics, 2008, 52 (8)
[5] New Results on the Equivalence of K-Functionals and Modulus of Continuity of Functions Defined on the Sobolev Space Constructed by the Generalized Jacobi-Dunkl Operator
El Mfadel, Ali
Melliani, Said
Elomari, M'hamed
ADVANCES IN MATHEMATICAL PHYSICS, 2022, 2022
[6] On the norms of generalized translation operators generated by the jacobi-dunkl operators
O. L. Vinogradov
Journal of Mathematical Sciences, 2012, 182 (5) : 603 - 616
[7] Generalized Wigner transform associated with the Jacobi-Dunkl operator and uncertainty principles
Mejjaoli, Hatem
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2024,
[8] On the equivalence of K-functionals and modulus of smoothness constructed by the generalized Fourier–Bessel transform
M. El Hamma
R. Daher
N. Djellab
Ch. Khalil
Afrika Matematika, 2022, 33
[9] Equivalence of K-functionals and modulus of smoothness generated by a Dunkl type operator on the interval (-1,1)
Saadi, Faouaz
Daher, Radouan
COMPTES RENDUS MATHEMATIQUE, 2023, 361 (01) : 1625 - 1633
[10] Equivalence of K-Functionals and Modulus of Smoothness for Fourier Transform
Daher, R.
El Hamma, M.
INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS, 2012, 3 (02): : 38 - 43

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