Abstract:
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. On the base of 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.
Citation:
S. S. Platonov, E. S. Belkina, “Equivalence of K-functionals and moduli of smoothness constructed by generalized Dunkl translations”, Izv. Vyssh. Uchebn. Zaved. Mat., 2008, no. 8, 3–15; Russian Math. (Iz. VUZ), 52:8 (2008), 1–11
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