Orthogonal Polynomials of Several Variables, 2nd Edition

Serving both as an introduction to the subject and as a reference, this book presents the theory in elegant form and with modern concepts and notation. It covers the general theory and emphasizes the classical types of orthogonal polynomials whose weight functions are supported on standard domains. The approach is a blend of classical analysis and symmetry group theoretic methods. Finite reflection groups are used to motivate and classify symmetries of weight functions and the associated polynomials. This revised edition has been updated throughout to reflect recent developments in the field. It contains 25% new material, including two brand new chapters on orthogonal polynomials in two variables, which will be especially useful for applications, and orthogonal polynomials on the unit sphere. The most modern and complete treatment of the subject available, it will be useful to a wide audience of mathematicians and applied scientists, including physicists, chemists and engineers.

Table of Contents

Chapter 1 Background
Chapter 2 Orthogonal Polynomials in Two Variables
Chapter 3 General Properties of Orthogonal Polynomials in Several Variables
Chapter 4 Orthogonal Polynomials on the Unit Sphere
Chapter 5 Examples of Orthogonal Polynomials in Several Variables
Chapter 6 Root Systems and Coxeter Groups
Chapter 7 Spherical Harmonics Associated with Reflection Groups
Chapter 8 Generalized Classical Orthogonal Polynomials
Chapter 9 Summability of Orthogonal Expansions
Chapter 10 Orthogonal Polynomials Associated with Symmetric Groups
Chapter 11 Orthogonal Polynomials Associated with Octahedral Groups, and Applications