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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 2006 Volume 337, Pages 134–164 (Mi znsl186)

This article is cited in 5 papers

On approximating periodic functions using linear approximation methods

A. S. Zhuk, V. V. Zhuk

Saint-Petersburg State University

Abstract: In the paper, a generalization of a known theorem by Hardy and Young is obtained; a formula interrelating the integral of a $2\pi$-periodic function over the period with the integral over the entire axis is established; new approximation characteristics for functions belonging to saturation classes of continuity modules of different orders for the spaces $L_p$ of periodic functions are provided, and some issues concerning approximation, in the uniform metric, of continuous periodic functions even with respect to each of their variables and having nonnegative Fourier coefficients are considered. Bibliography: 17 titles.

UDC: 517.5

Received: 02.05.2006


 English version:
Journal of Mathematical Sciences (New York), 2007, 143:3, 3090–3107

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