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arXiv · 2001.08796

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

Yurii Kolomoitsev·Maria Skopina
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Abstract

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

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Yurii Kolomoitsev, Maria Skopina. 2020-01-23. Approximation by sampling-type operators in $L_p$-spaces. https://doi.org/10.1002/mma.6222

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