Geodesic
On a class of $N$-dimensional trigonometric series
Matematičeskie zametki, Tome 63 (1998) no. 3, pp. 402-406.

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An analog of Fomin's well-known one-dimensional theorem is proved for trigonometric series of the form $$ \lambda_0+\sum_{l=1}^\infty\lambda_l\sum_{k\in lV\setminus(l-1)V}e^{ikx}, \qquad \lambda_l\to0 \quad\text{as}\quad l\to\infty, $$ given on an $N$-dimensional torus, where $V$ is some polyhedron in $\mathbb R^N$. 
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O. I. Kuznetsova. On a class of $N$-dimensional trigonometric series. Matematičeskie zametki, Tome 63 (1998) no. 3, pp. 402-406. http://geodesic.mathdoc.fr/item/MZM_1998_63_3_a9/

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