Titlebook: Geometry of the Unit Sphere in Polynomial Spaces; Jesús Ferrer,Domingo García,Juan B. Seoane Book 2022 The Author(s), under exclusive lice

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https://doi.org/10.1007/3-540-33200-6We investigate some geometrical properties of polynomials of degree 2 on non-balanced convex bodies with respect to the origin in ., providing an explicit formula to calculate their norm and a full description of the extreme points of the corresponding unit balls. We review all the cases considered up to now in the literature in this context.

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Space and Time in Special Relativity,This chapter is dedicated to the study of the geometry of polynomial spaces on . for certain values of ., ., presenting all known results for these classes of spaces.

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Quantum Foundations: General OutlookIn this chapter we focus on the extreme points of the unit ball of quadratic forms on . endowed with the octagonal and hexagonal norms.

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https://doi.org/10.1007/978-3-658-07196-7In this chapter we will show some results on the extreme points of the unit ball of certain polynomial spaces in arbitrary Banach spaces. More particularly, we are interested in studying integral, nuclear and orthogonally additive polynomials.

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