Five uniqueness questions for multiple trigonometric series are surveyed. If a multiple trigonometric series converges everywhere to zero in the sense of spherical convergence, of unrestricted rectangular convergence, or of iterated convergence, then that series must have every coefficient being zero. But the cases of square convergence and restricted rectangular convergence lead to open questions.
@article{1786,
title = {Uniqueness for higher dimensional trigonometric series},
journal = {CUBO, A Mathematical Journal},
volume = {4},
year = {2002},
language = {en},
url = {http://dml.mathdoc.fr/item/1786}
}
Marshall Ash, J. Uniqueness for higher dimensional trigonometric series. CUBO, A Mathematical Journal, Tome 4 (2002) . http://gdmltest.u-ga.fr/item/1786/