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 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 1972, Volume 12, Issue 4, Pages 413–419 (Mi mz9899)

A lower bound for $n$-diameters

I. F. Sharygin

M. V. Lomonosov Moscow State University

Abstract: 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.

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English version:
Mathematical Notes, 1972, 12:4, 680–684

Bibliographic databases:

UDC: 517.5

Citation: I. F. Sharygin, “A lower bound for $n$-diameters”, Mat. Zametki, 12:4 (1972), 413–419; Math. Notes, 12:4 (1972), 680–684

Citation in format AMSBIB
\Bibitem{Sha72} \by I.~F.~Sharygin \paper A lower bound for $n$-diameters \jour Mat. Zametki \yr 1972 \vol 12 \issue 4 \pages 413--419 \mathnet{http://mi.mathnet.ru/mz9899} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=322416} \zmath{https://zbmath.org/?q=an:0258.46021} \transl \jour Math. Notes \yr 1972 \vol 12 \issue 4 \pages 680--684 \crossref{https://doi.org/10.1007/BF01093673}