This article is cited in 16 papers

On the uniqueness of series in the Franklin system

G. G. Gevorkyan

Yerevan State University, Armenia

Abstract: We prove: a) a uniqueness theorem for everywhere convergent series in the Franklin system; b) a uniqueness theorem for Franklin series that converge in measure, whose least upper bound of the sequence of modules of partial sums is finite everywhere, except possibly on a countable set, and whose coefficients satisfy a certain necessary condition.
Bibliography: 16 titles.

Keywords: Franklin system, Cantor's theorem, uniqueness theorem.

UDC: 517.53

MSC: Primary 42C25; Secondary 42C10

Received: 01.12.2015 and 29.03.2016

DOI: 10.4213/sm8640

 English version: Sbornik: Mathematics, 2016, 207:12, 1650–1673

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