Approximation of infinitely differentiable periodic functions by interpolation trigonometric polynomials in integral metric

被引：0

作者：

Serdyuk A.S. ^{[1
]}

机构：

[1] Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

来源：

Ukrainian Mathematical Journal | 2001年 / 53卷 / 12期

关键词：

Periodic Function; Differentiable Function; Trigonometric Polynomial; Asymptotic Equality; Interpolation Trigonometric;

D O I：

10.1023/A:1015490906892

中图分类号：

学科分类号：

摘要：

We obtain asymptotic equalities for the upper bounds of approximations of periodic infinitely differentiable functions by interpolation trigonometric polynomials in the metric of L1 on the classes of convolutions. © 2001 Plenum Publishing Corporation.

引用

页码：2014 / 2026

页数：12

共 9 条

[1]

Stepanets A.I., Classification and Approximation of Periodic Functions [in Russian], (1987)

[2]

Stepanets O.I., Serdyuk A.S., An estimate of the residual of approximation by interpolation trigonometric polynomials on classes of infinitely differentiable functions, Theory of Approximation of Functions and Its Applications [in Ukrainian], pp. 446-460, (2000)

[3]

Korneichuk N.P., Extremal Problems of Approximation Theory [in Russian], (1976)

[4]

Nikol'skii S.M., Approximation of functions by trigonometric polynomials in the mean, Izv. Akad. Nauk SSSR, Ser. Mat., 10, 3, pp. 207-256, (1946)

[5]

Stepanets A.I., Classes of functions defined on the real axis and their approximation by entire functions. II, Ukr. Mat. Zh., 42, 2, pp. 210-222, (1990)

[6]

Stepanets A.I., Rate of convergence of Fourier series on the classes of ψ̄-integrals, Ukr. Mat. Zh., 49, 8, pp. 1069-1113, (1997)

[7]

Serdyuk A.S., Approximation of analytic functions by interpolation trigonometric polynomials in the metric of L, Boundary-Value Problems for Differential Equations [in Ukrainian], pp. 240-250, (1998)

[8]

Serdyuk A.S., Approximation of periodic functions of high smoothness by interpolation trigonometric polynomials in the metric of L<sub>1</sub>, Ukr. Mat. Zh., 52, 7, pp. 994-998, (2000)

[9]

Motornyi V.P., Approximation of periodic functions by interpolation polynomials in L<sub>1</sub>, Ukr. Mat. Zh., 42, 6, pp. 781-786, (1990)

← 1 →