Geodesic
Best approximation of functions in $L_p$ by polynomials on affine system
Sbornik. Mathematics, Tome 202 (2011) no. 2, pp. 279-306

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Estimates of the best $L_p$-approximation of functions by polynomials in an affine system (system of dilations and translations), which are similar to well-known estimates due to Ul'yanov and Golubov for approximations in the Haar system, are obtained. An analogue of A. F. Timan and M. F. Timan's inequality is shown to hold under certain conditions on the generating function of the affine system; this analogue fails for the Haar system for $1$. Bibliography: 10 titles.
Keywords: Haar system, system of dilations and translations, affine system, best approximation. 
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     author = {P. A. Terekhin},
     title = {Best approximation of functions in $L_p$ by polynomials on affine system},
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     url = {http://geodesic.mathdoc.fr/item/SM_2011_202_2_a4/}
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P. A. Terekhin. Best approximation of functions in $L_p$ by polynomials on affine system. Sbornik. Mathematics, Tome 202 (2011) no. 2, pp. 279-306. http://geodesic.mathdoc.fr/item/SM_2011_202_2_a4/