J. Bourgain, B. S. Kashin, “Uniform approximation of partial sums of a Dirichlet series by shorter sums and <nobr>$\Phi$</nobr>-widths”, Mat. Sb., 2012, Volume 203, Number 12,Pages <nobr>57

This article is cited in 2 papers

Uniform approximation of partial sums of a Dirichlet series by shorter sums and $\Phi$-widths

J. Bourgain^a, B. S. Kashin^b

^a Institute for Advanced Study, Princeton, NJ
^b Steklov Mathematical Institute of the Russian Academy of Sciences

Abstract: 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.

UDC: 517.537.72+511.332

MSC: 30B50, 41A46

Received: 27.08.2012

DOI: 10.4213/sm8176