Approximation by sampling-type operators in $L_p$-spaces

Abstract

Approximation properties of the sampling-type quasi-projection operators $Q_j(f,\phi ,\tilde{\phi })$ for functions $f$ from anisotropic Besov spaces are studied. Error estimates in $L_p$-norm are obtained for a large class of tempered distributions $\tilde{\phi }$ and a large class of functions $\phi$ under the assumptions that $\phi$ has enough decay, satisfies the Strang-Fix conditions and a compatibility condition with $\tilde{\phi }$. The estimates are given in terms of moduli of smoothness and best approximations.