Geodesic
Uniform approximation of partial sums of a~Dirichlet series by shorter sums and $\Phi$-widths
Sbornik. Mathematics, Tome 203 (2012) no. 12, pp. 1736-1760

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It is shown that each Dirichlet polynomial $P$ of degree $N$ which is bounded in a certain natural Euclidean norm, admits a nontrivial uniform approximation on the corresponding interval on the real axis by a Dirichlet polynomial with spectrum containing significantly fewer than $N$ elements. Moreover, this spectrum is independent of $P$. Bibliography: 19 titles.
Keywords: Dirichlet series, widths, $\varepsilon$-entropy. 
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     title = {Uniform approximation of partial sums of {a~Dirichlet} series by shorter sums and $\Phi$-widths},
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J. Bourgain; B. S. Kashin. Uniform approximation of partial sums of a~Dirichlet series by shorter sums and $\Phi$-widths. Sbornik. Mathematics, Tome 203 (2012) no. 12, pp. 1736-1760. http://geodesic.mathdoc.fr/item/SM_2012_203_12_a3/