FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2000, VOLUME 6, NUMBER 3, PAGES 813-829

On convergence of generalized systems similar to orthogonal ones

T. P. Lukashenko
T. V. Rodionov

Abstract

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For generalized expansion systems similar to orthogonal ones the analogs of the following properties of orthogonal systems are proved: Paley--Zygmund theorem on almost everywhere convergence under almost all orders of signs, Garsia theorem on existence of almost everywhere convergent rearrangement of series terms, Orlicz and Tandori theorems on unconditional convergence.

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Last modified: December 8, 2000