This article is cited in 3 papers

Brief communications

A sharp error estimate of the best approximation by algebraic polynomials in the weighted space $L_2(-1,1)$

R. Z. Dautov

Chair of Computational Mathematics, Kazan (Volga Region) Federal University, Kazan, Russia

Abstract: We obtain a sharp error estimate of the best approximation by algebraic polynomials in the Lebesgue space $L_2(-1,1)$ with the weight $1-x^2$ of degree $\lambda>-1$.

Keywords: best approximation, sharp estimate, weighted space.

UDC: 517.518

Received: 28.11.2012

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2013, 57:5, 51–53