V. A. Abilov, F. V. Abilova, M. K. Kerimov, “Sharp estimates for the convergence rate of Fourier series in terms of orthogonal polynomials in <nobr>$L_2((a,b),p(x))$</nobr>”, Zh. Vychisl. Mat. Mat. Fiz., 2009, Volume 49, Number 6,Pages <nobr>966

This article is cited in 14 papers

Sharp estimates for the convergence rate of Fourier series in terms of orthogonal polynomials in $L_2((a,b),p(x))$

V. A. Abilov^a, F. V. Abilova^b, M. K. Kerimov^c

^a Dagestan State University, ul. Gadzhieva 43a, Makhachkala, 367025, Russia
^b Dagestan State Technical University, pr. Kalinina 70, Makhachkala, 367015, Russia
^c Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119991, Russia

Abstract: Sharp estimates are given for the convergence rate of Fourier series in terms of classical orthogonal polynomials in some classes of functions characterized by a generalized modulus of continuity in the space $L_2((a,b),p(x))$. Expansions in terms of Laguerre, Hermite, and Jacobi polynomials are considered.

Key words: Fourier series, generalized modulus of continuity, width, generalized derivatives, expansions in terms of Laguerre, Hermite, Jacobi polynomials, convergence of series.

UDC: 519.651

Received: 05.12.2008
Revised: 28.12.2008