Sharp estimates for the convergence rate of double Fourier series in terms of orthogonal polynomials in the space L 2((a, b) x (c, d); p(x)q(y))

被引：5

作者：

Abilov, V. A. ^{[1
]}

Kerimov, M. K. ^{[2
]}

机构：

[1] Dagestan State Univ, Makhachkala 367025, Russia

[2] Russian Acad Sci, Dorodnicyn Comp Ctr, Moscow 119333, Russia

来源：

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS | 2009年 / 49卷 / 08期

基金：

俄罗斯基础研究基金会;

关键词：

orthogonal polynomials; double Fourier series; generalized modulus of continuity; Kolmogorov N-width; convergence rate estimate for double Fourier series;

D O I：

10.1134/S0965542509080028

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：1298 / 1302

页数：5

共 31 条

[1] Sharp estimates for the convergence rate of double Fourier series in terms of orthogonal polynomials in the space L2((a, b) × (c, d); p(x)q(y))
V. A. Abilov
M. K. Kerimov
Computational Mathematics and Mathematical Physics, 2009, 49 : 1298 - 1302
[2] Sharp estimates for the convergence rate of Fourier series in terms of orthogonal polynomials in L 2((a, b), p(x))
Abilov, V. A.
Abilova, F. V.
Kerimov, M. K.
COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2009, 49 (06) : 927 - 941
[3] Sharp estimates for the convergence rate of Fourier series in terms of orthogonal polynomials in L2((a, b), p(x))
V. A. Abilov
F. V. Abilova
M. K. Kerimov
Computational Mathematics and Mathematical Physics, 2009, 49 : 927 - 941
[4] Sharp estimates for the rate of convergence of double Fourier series in classical orthogonal polynomials
Abilov, V. A.
Abilov, M. V.
Kerimov, M. K.
COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2015, 55 (07) : 1094 - 1102
[5] Sharp estimates for the rate of convergence of double Fourier series in classical orthogonal polynomials
V. A. Abilov
M. V. Abilov
M. K. Kerimov
Computational Mathematics and Mathematical Physics, 2015, 55 : 1094 - 1102
[6] Sharp estimates for the convergence rate of “hyperbolic” partial sums of double fourier series in orthogonal polynomials
V. A. Abilov
M. K. Kerimov
Computational Mathematics and Mathematical Physics, 2012, 52 : 1497 - 1503
[7] Sharp Estimates for the Convergence Rate of "Hyperbolic" Partial Sums of Double Fourier Series in Orthogonal Polynomials
Abilov, V. A.
Kerimov, M. K.
COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2012, 52 (11) : 1497 - 1503
[8] Sharp estimates for the convergence rate of Fourier series of complex variable functions in L 2(D, p(z))
Abilov, V. A.
Abilova, F. V.
Kerimov, M. K.
COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2010, 50 (06) : 946 - 950
[9] Sharp estimates for the convergence rate of Fourier series of complex variable functions in L2(D, p(z))
V. A. Abilov
F. V. Abilova
M. K. Kerimov
Computational Mathematics and Mathematical Physics, 2010, 50 : 946 - 950
[10] On exact estimates of the convergence rate of fourier series for functions of one variable in the space L 2[-π, π]
Kerimov, M. K.
Selimkhanov, E. V.
COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2016, 56 (05) : 717 - 729

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