• R Daher

Articles written in Proceedings – Mathematical Sciences

• Uncertainty Principles for the Cherednik Transform

We shall investigate two uncertainty principles for the Cherednik transform on the Euclidean space $\mathfrak{a}$; Miyachi’s theorem and Beurling’s theorem. We give an analogue of Miyachi’s theorem for the Cherednik transform and under the assumption that $\mathfrak{a}$ has a hypergroup structure, an analogue of Beurling’s theorem for the Cherednik transform.

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

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 $\mathbb{R}^d$.

• # Proceedings – Mathematical Sciences

Current Issue
Volume 129 | Issue 5
November 2019

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019