This article is cited in 4 papers

A characterization of extremal elements in some linear problems

Vitalii V. Arestov<sup>ab

a</sup> 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.

Language: English

DOI: 10.15826/umj.2017.2.004

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