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 Ural Math. J., 2017, Volume 3, Issue 2, Pages 22–32 (Mi umj39)

A characterization of extremal elements in some linear problems

Vitalii V. Arestovab

a Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
b Ural Federal University, Ekaterinburg

Abstract: We give a characterization of elements of a subspace of a complex Banach space with the property that the norm of a bounded linear functional on the subspace is attained at those elements. In particular, we discuss properties of polynomials that are extremal in sharp pointwise Nikol'skii inequalities for algebraic polynomials in a weighted $L_q$-space on a finite or infinite interval.

Keywords: Complex Banach space, Bounded linear functional on a subspace, Algebraic polynomial, Pointwise Nikol'skii inequality.

 Funding Agency Grant Number Ural Branch of the Russian Academy of Sciences 15-16-1-4 This work was supported by the Program of the Ural Branch of the Russian Academy of Sciences (project no. 15-16-1-4).

DOI: https://doi.org/10.15826/umj.2017.2.004

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Citation: Vitalii V. Arestov, “A characterization of extremal elements in some linear problems”, Ural Math. J., 3:2 (2017), 22–32

Citation in format AMSBIB
\Bibitem{Are17} \by Vitalii~V.~Arestov \paper A characterization of extremal elements in some linear problems \jour Ural Math. J. \yr 2017 \vol 3 \issue 2 \pages 22--32 \mathnet{http://mi.mathnet.ru/umj39} \crossref{https://doi.org/10.15826/umj.2017.2.004} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=MR3746948} \elib{https://elibrary.ru/item.asp?id=32334095}