Geodesic
On a class of $N$-dimensional trigonometric series
Matematičeskie zametki, Tome 63 (1998) no. 3, pp. 402-406 
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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     title = {On a class of $N$-dimensional trigonometric series},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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 $\mathbb R^N$.

[1] Fomin G. A., “Ob odnom klasse trigonometricheskikh ryadov”, Matem. zametki, 23:2 (1978), 213–222 | MR | Zbl

[2] Kuznetsova O. I., “O silnykh srednikh Karlemana kratnykh trigonometricheskikh ryadov”, Ukr. matem. zh., 44:2 (1992), 275–279 | MR

[3] Gogoladze L. D., O summirovanii kratnykh trigonometricheskikh ryadov i sopryazhennykh funktsiyakh, Diss. ... d. f.-m. n., Tbilisi, 1984

[4] Nazarov F. L., Podkorytov A. N., “Povedenie konstant Lebega dvumernykh summ Fure po mnogougolnikam”, Algebra i analiz, 7:4 (1995), 214–238

[5] Stein I., Veis G., Vvedenie v garmonicheskii analiz na evklidovykh prostranstvakh, Mir, M., 1974 | Zbl

[6] Podkorytov A. N., “Poryadok rosta konstant Lebega summ Fure po poliedram”, Vestn. LGU. Matem., mekh., astron., 1982, no. 7, 110–111 | MR | Zbl