Supremum Norms for 2-Homogeneous Polynomials on Circle Sectors

摘要

We consider the Banach space of two homogeneous polynomials endowed with the supremum norm || ? ||_(D(β)) over circle sectors D(β) of angle β for several values of β ? [0, 2π]. We provide an explicit formula for || ? ||_(D(β)), 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.