This article is cited in 12 papers

Majorants and uniqueness of series in the Franklin system

G. G. Gevorkyan

Yerevan State University

Abstract: It is proved that if a series in the Franklin system converges almost everywhere to a function $f(t)$ and the distribution function of the majorant of partial sums satisfies the condition
$$ \operatorname{mes}\bigl\{t\in[0,1]:s(t)>\lambda\bigr\} =o\biggl(\frac 1\lambda\biggr) $$
as $\lambda\to\infty$, then this series is a Fourier series for Lebesgue integrable functions $f(t)$. In the general case the coefficients of the series are reconstructed by means of an $A$-integral.

UDC: 517.98

Received: 05.01.1995

DOI: 10.4213/mzm1747

 English version: Mathematical Notes, 1996, 59:4, 373–391

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