Abstract:We study approximation properties of linear sampling operators in the spaces Lp for 1 ≤ p < ∞. By means of the Steklov averages, we introduce a new measure of smoothness that simultaneously contains information on the smoothness of a function in Lp and discrete information on the behaviour of a function at sampling points. The new measure of smoothness enables us to improve and extend several classical results of approximation theory to the case of linear sampling operators. In particular, we obtain matching d… Show more
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