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

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      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

       

      M El Hamma1 R Daher1

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

       
  • Proceedings – Mathematical Sciences | News

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