This article is cited in 16 papers

Uniqueness theorems for Franklin series converging to integrable functions

G. G. Gevorkyan

Yerevan State University, Armenia

Abstract: The following results are proved: a) if a Franklin series converges everywhere to a finite integrable function, then it is the Fourier-Franklin series of this function; b) if a Franklin series converges to a finite integrable function everywhere except possibly at points in some countable set and if all its coefficients satisfy a certain necessary condition, then it is the Fourier-Franklin series of this function.
Bibliography: 16 titles.

Keywords: Franklin system, de la Vallée Poussin theorem, uniqueness theorem.

UDC: 517.53

MSC: 42B05

Received: 06.02.2017 and 28.06.2017

DOI: 10.4213/sm8922

 English version: Sbornik: Mathematics, 2018, 209:6, 802–822

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