Geodesic
A characterization of extremal elements in some linear problems
Ural mathematical journal, Tome 3 (2017) no. 2, pp. 22-32

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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, Pointwise Nikol'skii inequality.
Mots-clés : Algebraic polynomial 
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     author = {Vitalii V. Arestov},
     title = {A characterization of extremal elements in some linear problems},
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     url = {http://geodesic.mathdoc.fr/item/UMJ_2017_3_2_a3/}
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Vitalii V. Arestov. A characterization of extremal elements in some linear problems. Ural mathematical journal, Tome 3 (2017) no. 2, pp. 22-32. http://geodesic.mathdoc.fr/item/UMJ_2017_3_2_a3/