V. A. Abilov, M. K. Kerimov, “Sharp estimates for the convergence rate of double Fourier series in terms of orthogonal polynomials in the space <nobr>$L_2((a,b)\times(c,d);p(x)q(y)))$</nobr>”, Zh. Vychisl. Mat. Mat. Fiz., 2009, Volume 49, Number 8,Pages <nobr>1364

This article is cited in 6 papers

Sharp estimates for the convergence rate of double Fourier series in terms of orthogonal polynomials in the space $L_2((a,b)\times(c,d);p(x)q(y)))$

V. A. Abilov^a, M. K. Kerimov^b

^a Dagestan State University, ul. Gadzhieva 43a, Makhachkala, 367025, Russia
^b Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia

Abstract: Sharp estimates are obtained for the convergence rate of double Fourier series in terms of general orthogonal polynomials in some classes of functions and for the Kolmogorov $N$-widths of these classes. These results find applications in numerical analysis.

Key words: orthogonal polynomials, double Fourier series, generalized modulus of continuity, Kolmogorov $N$-width, convergence rate estimate for double Fourier series.

UDC: 519.651

Received: 03.02.2009