descriptionPublicationkeyboard_double_arrow_right Article 01 Dec 2009 English Publisher:Elsevier BVJournal:Journal of Approximation Theory, volume 161, pages 706-722 (issn: 0021-9045,

Authors: Grecu, Bogdan; Munoz, G.; Seoane, J.;

doi: 10.1016/j.jat.2008.12.001

Unconditional constants and polynomial inequalities

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Abstract

If \(P\) is a polynomial with real coefficients, \(|P|\) denotes the polynomial obtained from \(P\) replacing its coefficients by their absolute values. Inequalities between the norm of \(|P|\) and the norm of \(P\) on a convex subset are studied for some specific spaces of polynomials. The constants which appear in the studied inequalities happen to be the unconditional constants of the canonical bases of the considered spaces. The mentioned unconditional constants in the spaces of trinomials and respectively of homogeneous polynomials are established.

Related Organizations

Queen's University Belfast
United Kingdom
Complutense University of Madrid
Spain

Keywords

Mathematics(all), Extreme points, unconditional constant, /dk/atira/pure/subjectarea/asjc/2600/2604, name=Applied Mathematics, trinomials, name=Numerical Analysis, Homogeneous polynomials, /dk/atira/pure/subjectarea/asjc/2600/2603, Polynomial inequalities, /dk/atira/pure/subjectarea/asjc/2600/2600, extreme points, Inequalities in approximation (Bernstein, Jackson, Nikol'skiĭ-type inequalities), Numerical Analysis, homogeneous polynomials, Applied Mathematics, name=Analysis, Unconditional constant, polynomial inequalities, 004, name=General Mathematics, /dk/atira/pure/subjectarea/asjc/2600, /dk/atira/pure/subjectarea/asjc/2600/2612, Trinomials, Analysis

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