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- W2950795754 abstract "We prove a multivariate Whitney type theorem for the local anisotropic polynomial approximation in $L_p(Q)$ with $1leq pleq infty$. Here $Q$ is a $d$-parallelepiped in $RR^d$ with sides parallel to the coordinate axes. We consider the error of best approximation of a function $f$ by algebraic polynomials of fixed degree at most $r_i - 1$ in variable $x_i, i=1,...,d$, and relate it to a so-called total mixed modulus of smoothness appropriate to characterizing the convergence rate of the approximation error. This theorem is derived from a Johnen type theorem on equivalence between a certain K-functional and the total mixed modulus of smoothness which is proved in the present paper." @default.
- W2950795754 created "2019-06-27" @default.
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- W2950795754 date "2010-07-08" @default.
- W2950795754 modified "2023-09-23" @default.
- W2950795754 title "On Whitney type inequalities for local anisotropic polynomial approximation" @default.
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- W2950795754 doi "https://doi.org/10.48550/arxiv.1007.1362" @default.
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