Sharp estimates of best approximations in terms of holomorphic functions of weierstrass-type operators

被引：0

作者：

Vinogradov O.L. ^{[1
]}

机构：

[1] St. Petersburg State University, St. Petersburg

来源：

Journal of Mathematical Sciences | 2013年 / 193卷 / 1期

关键词：

Approximation Method; Holomorphic Function; Linear Approximation; Entire Function; Exponential Type;

D O I：

10.1007/s10958-013-1429-z

中图分类号：

学科分类号：

摘要：

Estimates of the form, where W is a kernel of a special type summable on ℝ, a function Φ is holomorphic in a neighborhood of the spectrum of W, and Aσ(f)P is the best approximation of a function f by entire functions of exponential type not greater than σ with respect to a seminorm P, are established. In some cases, for the uniform and integral norms the least possible constant K is found. The estimates are obtained by linear approximation methods. Bibliography: 13 titles. © 2013 Springer Science+Business Media New York.

引用

页码：8 / 31

页数：23

共 13 条

[1]

Akhiezer N.I., Lectures in Approximation Theory [in Russian], (1965)

[2]

Vinogradov O.L., Sharp Jackson-type inequalities for approximations of classes of convolutions by entire functions of exponential type, Algebra Analiz, 17, 4, pp. 56-111, (2005)

[3]

Vinogradov O.L., Sharp estimates of best approximations by deviations of Weierstrass-type integrals, Zap. Nauchn. Semin. POMI, 401, pp. 53-70, (2012)

[4]

Makarov B.M., Goluzina M.G., Lodkin A.A., Podkorytov A.N., Selected Problems in Real Analysis [in Russian], (2004)

[5]

Babenko A.G., Kryakin Y.V., Integral approximation of the characteristic: function of an interval and the Jackson inequality in C(T), Trudy Mat. Inst. Steklov, 15, 1, pp. 59-65, (2009)

[6]

Vinogradov O.L., Zhuk V.V., Estimates for functionals with a known moment sequence in terms of deviations of Steklov type means, Zap. Nauchn. Semin. POMI, 383, pp. 5-32, (2010)

[7]

Vinogradov O.L., Zhuk V.V., The rate of decrease of constants in Jackson type inequalities in dependence of the order of modulus of continuity, Zap. Nauchn. Semin. POMI, 383, pp. 33-52, (2010)

[8]

Timan A.F., Theory of Approximation of Functions of a Real Variable [in Russian], (1960)

[9]

Korneichuk N.P., Sharp Constants in Approximation Theory [in Russian], (1987)

[10]

Stefensen I.F., Interpolation Theory [Russian translation], (1935)

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