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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 2011 Volume 392, Pages 32–66 (Mi znsl4577)

This article is cited in 3 papers

Estimates for functionals with a known finite set of moments in terms of deviations of operators constructed with the use of the Steklov averages and finite differences

O. L. Vinogradov, V. V. Zhuk

Saint-Petersburg State University, Saint-Petersburg, Russia

Abstract: The paper presents a new technique for deriving the estimates mentioned in the title. In particular, this technique allows one to establish Jackson-type inequalities for moduli of continuity of arbitrary order with relatively small constants. The results obtained are valid in different spaces of periodic and nonperiodic functions.

Key words and phrases: best approximation, modulus of continuity, sharp constants, Steklov functions.

UDC: 517.5

Received: 12.08.2011


 English version:
Journal of Mathematical Sciences (New York), 2012, 184:6, 679–698

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