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On localization of functions in the Bernstein space

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Abstract

For ϱ > 0, let \(L^1 (\mathbb{R})\) be the closed subspace of L 1(ℝ) consisting of functions ƒ having the Fourier transforms ƒ concentrated in [−ϱ, ϱ]. Let a > 0. In this paper, we consider the problem of maximal localization of the L 1 norm on [−a, a] of functions from B 1 ϱ . More precisely, for a given a, we investigate the supremum of the quantity E a (ƒ) = ∫ a−a |ƒ(x)|dx over all ƒ from the unit ball of the space B 1 ϱ .

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Authors and Affiliations

  1. Insitute of Mathematics and Informatics, Akademijos 4, LT-08663, Vilnius, Lithuania

    S. Norvidas

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  1. S. Norvidas
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Correspondence to S. Norvidas.

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Translated from Lietuvos Matematikos Rinkinys, Vol. 47, No. 4, pp. 573–590, October–December, 2007.

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Norvidas, S. On localization of functions in the Bernstein space. Lith Math J 47, 470–483 (2007). https://doi.org/10.1007/s10986-007-0033-7

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  • DOI: https://doi.org/10.1007/s10986-007-0033-7

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