Abstract:
Estimates of the best Lp-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<p<∞.
Bibliography: 10 titles.
Keywords:
Haar system, system of dilations and translations, affine system, best approximation.
\Bibitem{Ter11}
\by P.~A.~Terekhin
\paper Best approximation of functions in $L_p$ by polynomials on affine system
\jour Sb. Math.
\yr 2011
\vol 202
\issue 2
\pages 279--306
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https://www.mathnet.ru/eng/sm7630
https://doi.org/10.1070/SM2011v202n02ABEH004146
https://www.mathnet.ru/eng/sm/v202/i2/p131
This publication is cited in the following 2 articles:
T. I. Zaitseva, “Multivariate tile B-splines”, Izv. Math., 87:2 (2023), 284–325
Kh. Kh. Kh. Al-Dzhourani, V. A. Mironov, P. A. Terekhin, “Affinnye sistemy funktsii tipa Uolsha. Polnota i minimalnost”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 16:3 (2016), 247–256
Citation in format AMSBIB
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