Geodesic
Sequences of partial sums of multiple trigonometric Fourier series
Sbornik. Mathematics, Tome 216 (2025) no. 3, pp. 368-385

Voir la notice de l'article provenant de la source Math-Net.Ru

Let $f$ be an integrable $2\pi$-periodic function of $d\ge2$ variables. For a bounded subset $A$ of the $d$-dimensional space let $S_A(f)$ denote the sum of terms of the Fourier series of $f$ with frequencies in $A$. The following problem is addressed: given a sequence $\{A_j\}$ of bounded convex sets, do there exist a function $f$ and a sequence $\{j_\nu\}$ such that $\lim_{\nu\to\infty} |S_{A_{j_\nu}} (f)|=\infty$ almost everywhere? Bibliography: 5 titles.
Keywords: convergence of multiple trigonometric Fourier series, convex set, lattice. 
@article{SM_2025_216_3_a7,
     author = {S. V. Konyagin},
     title = {Sequences of partial sums of multiple trigonometric {Fourier} series},
     journal = {Sbornik. Mathematics},
     pages = {368--385},
     publisher = {mathdoc},
     volume = {216},
     number = {3},
     year = {2025},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2025_216_3_a7/}
}
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S. V. Konyagin. Sequences of partial sums of multiple trigonometric Fourier series. Sbornik. Mathematics, Tome 216 (2025) no. 3, pp. 368-385. http://geodesic.mathdoc.fr/item/SM_2025_216_3_a7/