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arXiv · 2002.04247

Approximation properties of periodic multivariate quasi-interpolation operators

Yurii Kolomoitsev·Jürgen Prestin
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Abstract

We study approximation properties of general multivariate periodic quasi-interpolation operators, which are generated by distributions/functions $\widetilde{\varphi}_j$ and trigonometric polynomials $\varphi_j$. The class of such operators includes classical interpolation polynomials ($\widetilde\varphi_j$ is the Dirac delta function), Kantorovich-type operators ($\widetilde\varphi_j$ is a characteristic function), scaling expansions associated with wavelet constructions, and others. Under different compatibility conditions on $\widetilde\varphi_j$ and $\varphi_j$, we obtain upper and lower bound estimates for the $L_p$-error of approximation by quasi-interpolation operators in terms of the best and best one-sided approximation, classical and fractional moduli of smoothness, $K$-functionals, and other terms.

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Yurii Kolomoitsev, Jürgen Prestin. 2020-02-11. Approximation properties of periodic multivariate quasi-interpolation operators. https://arxiv.org/abs/2002.04247

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