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<p>This paper presents an explicit description of the extreme points in the space of quadratic forms, equipped with the supremum norm, defined over any triangle with one vertex at the origin. The geometric findings are then applied to compute the unconditional constant of the canonical basis of this space within a one-parameter family of triangles.</p>

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Geometry of the Space of Quadratic Forms on Triangles and Applications

  • 期刊论文

  • 发表日期：

    2025年8月11日

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  • G. Araújo,
  • A. García-Santiuste,
  • G. A. Muñoz-Fernández

摘要

This paper presents an explicit description of the extreme points in the space of quadratic forms, equipped with the supremum norm, defined over any triangle with one vertex at the origin. The geometric findings are then applied to compute the unconditional constant of the canonical basis of this space within a one-parameter family of triangles.