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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 2013 Volume 416, Pages 70–90 (Mi znsl5704)

This article is cited in 2 papers

Estimates of functionals by the second moduli of continuity of even derivatives

O. L. Vinogradov, V. V. Zhuk

St. Petersburg State University, St. Petersburg, Russia

Abstract: We establish an expansion of a function in terms of the second order differences of its derivatives. This expansion generalizes the well-known expansion in terms of the first order differences. Then, with the help of this expansion, we estimate some functionals by the second moduli of continuity. As particular cases of the estimates obtained, we have Jackson-type inequalities for approximations by entire fuctions of exponential type, trigonometric polynomials and splines in various function spaces. The constants in the new inequalities are smaller than those known before.

Key words and phrases: the second modulus of continuity, best approximation, Jackson inequalities.

UDC: 517.5

Received: 11.04.2013


 English version:
Journal of Mathematical Sciences (New York), 2014, 202:4, 526–540

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