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On some multiple functionseries and solution of the uniqueness problem for Pringsheim convergence of multiple trigonometric series

Sh. T. Tetunashvili

Tbilisi Ivane Javakhishvili State University

Abstract: Uniqueness theorems are proved for some multiple function series. A particular consequence of these theorems is the solution of a uniqueness problem for multiple trigonometric series. One result is the following proposition: any countable set is a set of uniqueness (for Pringsheim convergence) of $d$-fold trigonometric series $(d\geqslant 2)$.

UDC: 517.5

MSC: Primary 42B05; Secondary 42C05

Received: 09.07.1990

 English version: Mathematics of the USSR-Sbornik, 1992, 73:2, 517–534

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