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Uniqueness Theorem for Multiple Franklin Series

G. G. Gevorkyan

Yerevan State University

Abstract: The paper presents the proof of the uniqueness theorem for multiple series in the Franklin system that converge in measure and whose majorant of cubic partial sums with numbers $2^\nu$ satisfies a certain necessary condition. This result is new in the one-dimensional case as well.

Keywords: multiple series, Franklin system, uniqueness.

Received: 27.08.2015
Revised: 26.01.2016

DOI: 10.4213/mzm10901

 English version: Mathematical Notes, 2017, 101:2, 219–229

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