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A complete study of the geometry of 2-homogeneous polynomials on circle sectors
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas ( IF 1.8 ) Pub Date : 2020-06-27 , DOI: 10.1007/s13398-020-00892-6
L. Bernal-González , G. A. Muñoz-Fernández , D. L. Rodríguez-Vidanes , J. B. Seoane-Sepúlveda

We consider the Banach space of two homogeneous polynomials endowed with the supremum norm $$\Vert \cdot \Vert _{D(\beta )}$$ ‖ · ‖ D ( β ) over circle sectors $$D(\beta )$$ D ( β ) of all possible angles $$\beta \in [0,2\pi ]$$ β ∈ [ 0 , 2 π ] . We provide an explicit formula for $$\Vert \cdot \Vert _{D(\beta )}$$ ‖ · ‖ 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 generalizes a previously published paper and it has a number of applications.

中文翻译:

圆扇区上 2 齐次多项式的几何学的完整研究

我们考虑在圆扇区 $$D(\beta )$ 上具有最高范数的两个齐次多项式的 Banach 空间 $$\Vert \cdot \Vert _{D(\beta )}$$ ‖ · ‖ D ( β ) $D ( β ) 所有可能的角度 $$\beta \in [0,2\pi ]$$ β ∈ [ 0 , 2 π ] 。我们为 $$\Vert \cdot \Vert _{D(\beta )}$$ ‖ · ‖ D ( β ) 提供了一个明确的公式,对相应单位球的极值点的完整描述,以及参数化和它们的单位球体的图。这项工作概括了以前发表的论文,它有许多应用。
更新日期:2020-06-27
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