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Supremum Norms for 2-Homogeneous Polynomials on Circle Sectors

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Muñoz-Fernández, Gustavo A. and Pellegrino, D. and Seoane-Sepúlveda, Juan B. and Weber, A. (2014) Supremum Norms for 2-Homogeneous Polynomials on Circle Sectors. Journal of Convex Analysis, 21 (3). pp. 743-764. ISSN 0944-6532

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Official URL: http://www.heldermann-verlag.de/jca/jca21/jca1310_b.pdf



Abstract

We consider the Banach space of two homogeneous polynomials endowed with the supremum norm parallel to . parallel to(D(beta)) over circle sectors D(beta) of angle beta for several values of beta is an element of [0, 2 pi]. We provide an explicit formula for parallel to . parallel to(D(beta)), a full description of the extreme points of the corresponding unit balls, and a parametrization and a plot of their unit spheres. This work is an extension of a series of papers on the same topic published in the last decade and it has a number of applications to obtain polynomial-type inequalities


Item Type:Article
Uncontrolled Keywords:Bernstein and Markov inequalities; Unconditional constants; Polarizations constants; Polynomial inequalities; Homogeneous polynomials; Extreme points
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:28163
Deposited On:10 Feb 2015 09:27
Last Modified:28 Nov 2016 09:27

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