V. A. Abilov, F. V. Abilova, M. K. Kerimov, “Sharp estimates for the rate of convergence of Fourier series of functions of a complex variable in the space <nobr>$L\sb 2(D,p(z))$</nobr>”, Zh. Vychisl. Mat. Mat. Fiz., 2010, Volume 50, Number 6,Pages <nobr>999

This article is cited in 17 papers

Sharp estimates for the rate of convergence of Fourier series of functions of a complex variable in the space $L\sb 2(D,p(z))$

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

^a Daghestan State University, ul. Gadzhieva 43a, Makhachkala, 367025 Russia
^b Daghestan 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 derived for the convergence rate of Fourier series in terms of orthogonal systems of functions for certain classes of complex variable functions, and the Kolmogorov $N$-widths of these classes are determined. These issues find applications in numerical analysis methods.

Key words: orthogonal system of functions, completeness, Fourier series in terms of orthogonal systems, generalized modulus of continuity, Kolmogorov $N$-width, sharp estimates of convergence rate.

UDC: 519.651

Received: 06.10.2009