Some problems of approximation theory in the spacesL
p
on the line with power weight |
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Authors: | Iong Ping Li Chun Mei Su V I Ivanov |
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Institution: | 1. Beijing Normal University, Beijing, China 2. Tula State University, Tula, Russia
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Abstract: | 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. |
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