Geodesic
A lower bound for $n$-diameters
Matematičeskie zametki, Tome 12 (1972) no. 4, pp. 413-419 
I. F. Sharygin. A lower bound for $n$-diameters. Matematičeskie zametki, Tome 12 (1972) no. 4, pp. 413-419. http://geodesic.mathdoc.fr/item/MZM_1972_12_4_a7/
@article{MZM_1972_12_4_a7,
     author = {I. F. Sharygin},
     title = {A lower bound for $n$-diameters},
     journal = {Matemati\v{c}eskie zametki},
     pages = {413--419},
     year = {1972},
     volume = {12},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1972_12_4_a7/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $\mathrm{D}$ be a subset of the $s$-dimensional lattice $\mathrm{Z^s}$, $\mathrm{M=M(D)}$ the number of elements in $\mathrm{D}$, $\mathscr{T}_D$ the space of trigonometric polynomials on the torus $\mathrm{T}^{\mathrm{s}}$ with spectrum concentrated in $\mathrm{D}$ and having unit norm in $\mathrm{L_2(T^{s})}$. In this paper we give the following bound for the Gel'fand diameter: $d^n(\mathscr{T}_D, C(T^s))\geqslant\sqrt{\frac M2}-\sqrt{\frac N2}$. This bound is subsequently used for actual functional classes.