Geometry of the Unit Sphere in Polynomial Spaces (SpringerBriefs in Mathematics)

Contents
1 Introduction
2 Polynomials of Degree n
	2.1 On the Real Line
		2.1.1 Polynomials Bounded by a Majorant
	2.2 On the Complex Plane
3 Spaces of Trinomials
	3.1 On the Real Line with the Supremum Norm
		3.1.1 The Geometry of Bm,n,∞ for Odd Numbers m,n
		3.1.2 The Geometry of Bm,n,∞ for m Odd and n Even
		3.1.3 The Geometry of Bm,n,∞ for m Even and n Odd
		3.1.4 The Geometry of Bm,n,∞ for Even Numbers m,n
	3.2 On the Real Line with the Lp-Norm
	3.3 On the Real Plane
		3.3.1 The Geometry of B2n,n,∞,2 for n Odd
		3.3.2 The Geometry of B2n,n,∞,2 for n Even
		3.3.3 The Geometry of Bm,n,∞,2 for m Odd
	3.4 On the Complex Plane
4 Polynomials on Non-Balanced Convex Bodies
	4.1 The Simplex
		4.1.1 Polynomials of Degree at Most 2
	4.2 The Unit Square
	4.3 Circular Sectors
		4.3.1 The Geometry of BD(β) When β≥π
		4.3.2 The Geometry of BD(β) When β=π4,π2,3π4
		4.3.3 The General Case of BD(β)
5 Sequence Banach Spaces
	5.1 The Space 12
	5.2 The Space ∞2
	5.3 The Space p2 when 12
6 Polynomials with the Hexagonal and Octagonal Norms
	6.1 Octagonal Norm
	6.2 Hexagonal Norm
7 Hilbert Spaces
	7.1 The Real and Complex Case for 2-Homogeneous Polynomials
	7.2 Polynomials of Degree n
8 Banach Spaces
	8.1 Integral and Nuclear Polynomials
	8.2 Orthogonally Additive Polynomials
9 Applications
	9.1 Bernstein-Markov Type Inequalities
	9.2 Polarization Constants
	9.3 Unconditional Constants
	9.4 Bohnenblust–Hille and Hardy–Littlewood Constants
		9.4.1 On the Complex Case
		9.4.2 On the Real Case
References