On series arising from the approximation of periodic differentiable functions by Poisson integrals

被引：0

作者：

V. P. Zastavnyi

机构：

[1] Donetsk National University,

来源：

Mathematical Notes | 2009年 / 86卷

关键词：

periodic differentiable function; Poisson integral; Bernoulli polynomial; Euler polynomial; Stirling numbers; conformal mapping;

D O I：

暂无

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学科分类号：

摘要：

For series of special form, we obtain an expansion in powers of the parameter. The coefficients of the expansion can be written out explicitly in terms of Bernoulli polynomials. In a particular case, we obtain an expansion in powers of the parameter of upper bounds for deviations of periodic differentiable functions from their Poisson integrals.

引用

共 12 条

[1] Timan A. F.(1950)A precise estimate of the remainder in the approximation of differentiable functions by Poisson integrals Dokl. Akad. Nauk SSSR 74 17-20
[2] Shtark É. L. L.(1973)The complete asymptotic expansion for the supremum of the deviation of functions in Lip1 from their Abel-Poisson singular integrals Mat. Zametki 13 21-28
[3] Zhigallo K. M.(2002)The complete asymptotics of the deviation from the class of differentiable functions of the set of their harmonic Poisson integrals Ukrain.Mat. Zh. 54 43-52
[4] Kharkevich Yu. I.(1975)Certain properties of operators of Abel-Poisson type Mat. Zametki 17 169-180
[5] Baskakov V. A.(1969)Approximation of functions satisfying Lipschitz conditions by Fejer sums Ukrain.Mat. Zh. 21 334-343
[6] Telyakovskii S. A.(2000)On the approximation of functions from the Hölder class by their biharmonic Poisson integrals Ukrain.Mat. Zh. 52 971-974
[7] Zhigallo K. M.(2002)Approximation of differentiable periodic functions by their biharmonic Poisson integrals Ukrain. Mat. Zh. 54 1213-1219
[8] Kharkevich Yu. I.(2007)Asymptotics of the values of approximations in the mean for classes of differentiable functions by using biharmonic Poisson integrals Ukrain.Mat. Zh. 59 1105-1115
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