Estimate of 𝐾-Functionals and Modulus of Smoothness Constructed by Generalized Spherical Mean Operator

Proceedings Mathematical Sciences

M El Hamma²  R Daher¹ 

[1] $$;Department of Mathematics, Faculty of Sciences Aïn Chock, University of Hassan II, Casablanca, Morocco$$

关键词: Dunkl operator;    generalized spherical mean operator;    𝐾-functional;    modulus of smoothness.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

Using a generalized spherical mean operator, we define generalized modulus of smoothness in the space $L^2_k(mathbb{R}^d)$. Based on the Dunkl operator we define Sobolev-type space and 𝐾-functionals. The main result of the paper is the proof of the equivalence theorem for a 𝐾-functional and a modulus of smoothness for the Dunkl transform on $mathbb{R}^d$.

【 授权许可】

Unknown