### A CHARACTERIZATION OF EXTREMAL ELEMENTS IN SOME LINEAR PROBLEMS

#### 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.

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