A characterization of extremal elements in some linear problems

Vitalii V. Arestov

Ural mathematical journal, Tome 3 (2017) no. 2, pp. 22-32

Résumé

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.

Détail

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

Bibliographie

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