A. S. Belov, S. A. Telyakovskii, “Refinement of the Dirichlet–Jordan and Young's theorems on Fourier series of functions of bounded variation”, Mat. Sb., 2007, Volume 198, Number 6,Pages <nobr>25

This article is cited in 13 papers

Refinement of the Dirichlet–Jordan and Young's theorems on Fourier series of functions of bounded variation

A. S. Belov^a, S. A. Telyakovskii^b

^a Ivanovo State University
^b Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: Necessary and sufficient conditions on an increasing sequence of positive integers $\{n_j\}$ ensuring that the Fourier series of a function of bounded variation has uniformly bounded sums of the absolute values of the blocks of terms with harmonics from $n_j$ to $n_{j+1}-1$ are established.
Bibliography: 9 titles.

UDC: 517.518.45

MSC: 42A20, 26A45

Received: 27.07.2006 and 20.10.2006

DOI: 10.4213/sm2420