Rectangular and iterated convergence of multiple trigonometric series (Q1332613)

The author presents a proof of the result by \textit{Sh. T. Tetunashvili} [Mat. Sb. 182, No. 8, 1158-1176 (1991; Zbl 0742.42013)] that says that if a multiple trigonometric series converges rectangularly everywhere, then it converges iteratively everywhere to the same limit. In particular, this yields the solution of the uniqueness problem; namely, if a multiple trigonometric series converges rectangularly everywhere to zero, then all its coefficients are zero. The author gives a detailed proof in two dimensions.