This article is cited in 1 paper

Sequences of rectangular Fourier sums of continuous functions with given majorants of the mixed moduli of smoothness

O. V. Davydov

Dnepropetrovsk State University

Abstract: Approximation by the rectangular Fourier sums $S_N(f)$ is studied for classes of functions of several variables defined in terms of the orders of decrease of the mixed moduli of smoothness. The problem of the existence of a single (independent of $N$) function $f$ on which the order of the approximation in the corresponding class is realized is solved.

UDC: 517.5

MSC: Primary 42B05; Secondary 26B05

Received: 27.09.1995

DOI: 10.4213/sm143

 English version: Sbornik: Mathematics, 1996, 187:7, 981–1004

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