Equivalence of K-functionals and modulus of smoothness constructed by generalized Dunkl translations

被引：0
|
作者：
E. S. Belkina
S. S. Platonov
机构：
[1] Petrozavodsk State University,
来源：
Russian Mathematics | 2008年 / 52卷 / 8期
关键词：
Dunkl operator; generalized Dunkl translation; K-functional; modulus of smoothness;
D O I：
10.3103/S1066369X0808001X
中图分类号：
学科分类号：
摘要：
In a Hilbert space L2,α:= L2(ℝ, |x|2α+1dx), 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 L2,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.
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