Equivalence of K-functionals and modulus of smoothness constructed by generalized Dunkl translations |
| |
Authors: | E. S. Belkina S. S. Platonov |
| |
Affiliation: | (1) Petrozavodsk State University, pr. Lenina 33, Petrozavodsk, 185640, Russia |
| |
Abstract: | In a Hilbert space L 2,α := L 2(?, |x|2α+1 dx), α > ? 1/2, we study the generalized Dunkl translations constructed by the Dunkl differential-difference operator. Using the generalized Dunkl translations, we define generalized modulus of smoothness in the space L 2,α . Based on the Dunkl operator we define Sobolev-type spaces 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. |
| |
Keywords: | Dunkl operator generalized Dunkl translation K-functional modulus of smoothness |
本文献已被 SpringerLink 等数据库收录! |
|