Geodesic
Some Problems of Approximation Theory in the Spaces~$L_p$ on the Line with Power Weight
Matematičeskie zametki, Tome 90 (2011) no. 3, pp. 362-383

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In the spaces $L_p$ on the line with power weight, we study approximation of functions by entire functions of exponential type. Using the Dunkl difference-differential operator and the Dunkl transform, we define the generalized shift operator, the modulus of smoothness, and the $K$-functional. We prove a direct and an inverse theorem of Jackson–Stechkin type and of Bernstein type. We establish the equivalence between the modulus of smoothness and the $K$-functional.
Keywords: Dunkl difference-differential operator, entire function, Dunkl transform, generalized shift operator, modulus of smoothness, the spaces $L_p$, Jackson–Stechkin theorem. 
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     author = {Iong Ping Li and Chun Mei Su and V. I. Ivanov},
     title = {Some {Problems} of {Approximation} {Theory} in the {Spaces~}$L_p$ on the {Line} with {Power} {Weight}},
     journal = {Matemati\v{c}eskie zametki},
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Iong Ping Li; Chun Mei Su; V. I. Ivanov. Some Problems of Approximation Theory in the Spaces~$L_p$ on the Line with Power Weight. Matematičeskie zametki, Tome 90 (2011) no. 3, pp. 362-383. http://geodesic.mathdoc.fr/item/MZM_2011_90_3_a3/