1- https://doi.org/10.1134/s0001434624070216
Generalized One-Dimensional Dunkl Transform in Direct Problems of Approximation Theory
- Aug 1, 2024
- Mathematical Notes
- V I Ivanov
Abstract
On the real line, we study the generalized Dunkl harmonic analysis depending on a parameter $$r\in\mathbb{N}$$ . The case of $$r=0$$ corresponds to the usual Dunkl harmonic analysis. All constructions depend on the parameter $$r\ge 1$$ . The differences and moduli of smoothness are defined using a generalized translation operator. The Sobolev space and the $$K$$ -functional are defined using a differential-difference operator. An approximate Jackson-type inequality is proved. The equivalence of the $$K$$ -functional and the modulus of smoothness is established.
