Publication: Supremum Norms for 2-Homogeneous Polynomials on Circle Sectors
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2014
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Heldermann Verlag
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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
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