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

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/124/02/0235-0242

• # Keywords

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

• # Abstract

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 $\mathbb{R}^d$.

• # Author Affiliations

1. Department of Mathematics, Faculty of Sciences Aïn Chock, University of Hassan II, Casablanca, Morocco

• # Proceedings – Mathematical Sciences

Current Issue
Volume 129 | Issue 5
November 2019

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019