On some multiple functionseries and solution of the uniqueness problem for Pringsheim convergence of multiple trigonometric series
Sbornik. Mathematics, Tome 73 (1992) no. 2, pp. 517-534
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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 $(d\geqslant 2)$.
@article{SM_1992_73_2_a13,
author = {Sh. T. Tetunashvili},
title = {On some multiple functionseries and solution of the uniqueness problem for {Pringsheim} convergence of multiple trigonometric series},
journal = {Sbornik. Mathematics},
pages = {517--534},
year = {1992},
volume = {73},
number = {2},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1992_73_2_a13/}
}
TY - JOUR AU - Sh. T. Tetunashvili TI - On some multiple functionseries and solution of the uniqueness problem for Pringsheim convergence of multiple trigonometric series JO - Sbornik. Mathematics PY - 1992 SP - 517 EP - 534 VL - 73 IS - 2 UR - http://geodesic.mathdoc.fr/item/SM_1992_73_2_a13/ LA - en ID - SM_1992_73_2_a13 ER -
%0 Journal Article %A Sh. T. Tetunashvili %T On some multiple functionseries and solution of the uniqueness problem for Pringsheim convergence of multiple trigonometric series %J Sbornik. Mathematics %D 1992 %P 517-534 %V 73 %N 2 %U http://geodesic.mathdoc.fr/item/SM_1992_73_2_a13/ %G en %F SM_1992_73_2_a13
Sh. T. Tetunashvili. On some multiple functionseries and solution of the uniqueness problem for Pringsheim convergence of multiple trigonometric series. Sbornik. Mathematics, Tome 73 (1992) no. 2, pp. 517-534. http://geodesic.mathdoc.fr/item/SM_1992_73_2_a13/
[1] Geiringer H., “Trigonometrische Doppelreihen”, Monat. für Math., 28 (1918), 65–144 | MR
[2] Talalyan A. A., “O edinstvennosti kratnykh trigonometricheskikh ryadov”, Matem. sb., 132 (174) (1987), 104–130 | MR | Zbl
[3] Ash J., Welland G., “Convergence, uniqueness and summability of multiple trigonometric series”, Trans. Amer. Math. Soc., 163 (1972), 401–436 | DOI | MR | Zbl
[4] Gogoladze L. D., “Ob ogranichennosti skhodyaschikhsya srednikh kratnykh funktsionalnykh ryadov”, Matem. zametki, 34:6 (1983), 845–855 | MR | Zbl