Intro
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,[infinity] for Odd Numbers m,n
3.1.2 The Geometry of Bm,n,[infinity] for m Odd and n Even
3.1.3 The Geometry of Bm,n,[infinity] for m Even and n Odd
3.1.4 The Geometry of Bm,n,[infinity] 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,[infinity],2 for n Odd

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